GOD Himself makes the answer to this question quite clear to anyone who will believe in The Bible as The Word of God… Anyone who will receive the teachings of HIS chosen teachers (Moses and the Prophets, Jesus Christ- the only begotten son of God, and The Apostles of The Lord Jesus)- these are the teachers that HE (God) has sent for us to learn from today:
John 3:33 (KJV)
He that hath received His testimony hath set to his seal that God is true.
1 John 5:9 (KJV)
If we receive the witness of men, the witness of God is greater: for this is the witness of God which he hath testified of his Son.
John 10:5 (KJV)
“And a stranger will they not follow, but will flee from him: for they know not the voice of strangers… … …
… … …  My sheep hear my voice, and I know them, and they follow me”
It is GOD Himself that teaches us about The Way of Life that HE defines as “Christianity”. He does so, through the teachers HE CHOSE- His holy Apostles’…
Notice what Paul writes concerning this very point:
Hebrews 1:1-2 (KJV)
God, who at sundry times and in divers manners spake in time past unto the fathers by the prophets,  Hath in these last days spoken unto us by his Son, whom he hath appointed heir of all things, by whom also he made the worlds…
Paul tells us that it was (and is to this day) GOD speaking- NOT the man that is writing these things…
Are we willing to accept this- as the churches of the apostles’ time did?
1 Thessalonians 2:13 (KJV)
For this cause also thank we God without ceasing, because, when ye received the word of God which ye heard of us, ye received it not as the word of men, but as it is in truth, THE WORD OF GOD, which effectually worketh also IN YOU THAT BELIEVE.
So, once we establish The Bible as The Word of God, and not of men- we can then look for the answer (since we will not feel that we should alter the word that is from God)…
Again, the question is- Does The Law of God apply for the Christian in their life? Is our daily life as a Christian to be shaped according to The Law of God?
First, look at what Paul writes to us about The Law of God:
1 Tim. 1:8-11 (KJV)
But we know that The Law is good, IF a man use it lawfully;  Knowing this, that the law is not made for a righteous man, BUT for the lawless and disobedient, for the ungodly and for sinners, for unholy and profane, for murderers of fathers and murderers of mothers, for manslayers,  For whoremongers, for them that defile themselves with mankind, for menstealers, for liars, for perjured persons, and if there be any other thing that is contrary to sound doctrine;  According to the glorious gospel of the blessed God, which was committed to my trust.
– Notice that Paul states The Law of God stands against (convicts) anyone who is “lawless”… and he says that anyone who is lawless GOES “CONTRARY TO the sound teaching, according to THE GLORIOUS GOSPEL of the blessed God”
Why did Paul write that, “The Law was not made for a righteous man”?
Look at something else that Paul taught, with this in mind, and we find the answer:
Galatians 5:22-25 (KJV)
But the fruit of the Spirit is LOVE, joy, peace, longsuffering, gentleness, goodness, faith,  Meekness, temperance: against such THERE IS NO LAW.  And they that are Christ’s have crucified the flesh with the affections and lusts.  If we live in the Spirit, let us also walk in the Spirit.
Notice what Paul said just before this — back up a few verses:
 This I say then, Walk in the Spirit, and ye shall not fulfil the lust of the flesh.
 For the flesh lusteth against the Spirit, and the Spirit against the flesh: and THESE ARE CONTRARY THE ONE TO THE OTHER: so that ye cannot do the things that ye would.
 But IF ye be led of the Spirit, ye are not under the law.
 Now the works of the flesh are manifest, which are these; Adultery, fornication, uncleanness, lasciviousness,  Idolatry, witchcraft, hatred, variance, emulations, wrath, strife, seditions, heresies,  Envyings, murders, drunkenness, revellings, AND SUCH LIKE: of the which I tell you before, as I have also told you in time past, that they which do such things shall not inherit the kingdom of God.
Notice, the works of The Spirit (“If we live in the Spirit, let us also walk in the Spirit“)- “AGAINST SUCH THERE IS NO LAW of God” (the righteous man has no Law of God THAT CONVICTS HIM)… BUT, when it comes to “the works of the flesh“- against such THERE IS The Law.
The Law of God condemns (judges as wrong and worthy of death) “the works of the flesh” (the one walking CONTRARY TO The Law of God / “the glorious gospel of the blessed God”- (this person is labeled as unrighteous by God in His Word)…
The Law of God reveals SIN as SINFUL:
Romans 7:7-8 (NASB)
What shall we say then? Is the Law sin? May it never be! On the contrary, I would not have come to know sin except through the Law; for I would not have known about coveting if the Law had not said, “You shall NOT COVET.”
Paul also points out:
Romans 7:14 (NASB)
For we know that The Law IS SPIRITUAL; BUT I AM OF FLESH, SOLD INTO BONDAGE TO SIN.
And again here:
Galatians 2:17-20 (KJV)
But if, while we seek to be justified by Christ, we ourselves also are found SINNERS,
1 John 3:4 (KJV)
Whosoever committeth sin transgresseth also the law: for SIN IS the transgression of the law.
But if, while we seek to be justified by Christ, we ourselves also are found SINNERS, is therefore Christ the minister of sin? GOD FORBID.
 FOR IF I build again the things which I destroyed, I make myself a transgressor… …
Romans 6:6 (KJV)
Knowing this, that our old man is crucified with him, that the body of sin might be destroyed, THAT HENCEFORTH WE SHOULD NOT SERVE SIN.
1 John 3:4 (KJV)
Whosoever committeth sin transgresseth also the law: for SIN IS the transgression of the law.
Col. 2:11-12 (KJV)
… In whom also ye are circumcised with the circumcision made without hands, in putting off the body of the sins of the flesh BY the circumcision of Christ:  Buried with him in baptism, wherein also ye are risen with him through the faith of the operation of God, who hath raised him from the dead.
…  For I through the law am dead to the law, THAT I might live unto God.
 I AM CRUCIFIED WITH CHRIST: nevertheless I live; yet not I, but Christ liveth in me: and THE LIFE WHICH I NOW LIVE IN THE FLESH I live by the faith of the Son of God, who loved me, and gave himself for me.
Notice – we, as Christians, are to be baptized into a baptism of REPENTANCE FROM SIN:
Acts 2:38 (KJV)
Then Peter said unto them, REPENT, AND BE BAPTIZED every one of you in the name of Jesus Christ FOR THE REMISSION OF SINS, and ye shall receive the gift of the Holy Ghost.
The Baptism INTO the Name of Jesus Christ is a baptism of REPENTANCE FROM SIN:
“… for SIN IS the transgression of the law.”
Acts 11:18 (KJV)
… When they heard these things, they held their peace, and glorified God, saying, Then hath God also to the Gentiles granted REPENTANCE UNTO LIFE.
The baptism is the symbolism of our commitment (our vow) to God that we have committed our lives to TURNING AWAY from SIN… THIS is our side of the agreement for The New Covenant (in order to attain “Grace“).
Saint Paul teaches us that our “Baptism” (the true Christian baptism) is a symbolic deed representing THE BURIAL of our “FLESHLY” body
Gal. 5:19… “Now the WORKS OF THE FLESH are manifest, which ARE THESE; Adultery, fornication, uncleanness, lasciviousness,  Idolatry, witchcraft, hatred, variance, emulations, wrath, strife, seditions, heresies,  Envyings, murders, drunkenness, revellings, AND SUCH LIKE: of the which I tell you before, as I have also told you in time past, that they which do such things shall not inherit the kingdom of God.)…
Christ Jesus and ALL of His holy Apostles teach us REPENTANCE FROM SIN (turning away from breaking God’s holy Commandments/Law)…
The breaking of God’s holy Commandments are referred to by Paul as, “the works of the flesh“, and “The Body of SIN“…
The Breaking God’s Law would then be A VIOLATION TO OUR AGREEMENT WITH GOD that we made when we chose the Baptism of Repentance from dead works (the burial of dead works in this life)… THIS IS the baptism that the Apostles of The Lord Jesus teach in their writings that saves us; the baptism into the name of Jesus Christ “FOR REMISSION OF SINS” by the first step of agreeing to “REPENT”…
– “that the body of sin might be destroyed”
– “THAT HENCEFORTH”-(or, ‘from this time forward’) “we should not serve sin”
So- the answer is clearly given in God’s Word.
The Christian- the one that is “under Grace”- will be found PRACTICING OBEDIENCE to the holy Law of God; since the baptism we are to be baptized with in Jesus’ name is a baptism for REPENTANCE from “Sin” (repentance- turning away- from the breaking of God’s Law).
Even though we are taught that it is not the works of The Law that will “justify” us (since we all fall short by “sin”, and require GRACE for justification- grace is the forgiveness in Jesus’ name that we receive upon our repentance toward God from the sin that we commit)- it is not the works that justify us, but rather- THE WORKS are what VERIFY that we DO in fact have THE FAITH THAT SAVES:
Galatians 5:6 (KJV)
For in Jesus Christ neither circumcision availeth any thing, nor uncircumcision; but FAITH which worketh by love.
James 2:22 (NASB)
You see that faith was working WITH HIS WORKS, and as a result of the works, faith was perfected;
James 2:18 (NASB)
… “You have faith, and I have works; show me your faith without the works, and I will show you MY FAITH BY MY WORKS.”
Paul says that THE KIND OF FAITH that a true Christian is to be demonstrating, is one that, “works by love”.
Paul has just taught us that FAITH THAT EXISTS WITHOUT LOVE IS A BROKEN FAITH…
What is love?
1 John 5:3 (NASB)
For THIS is the love of God, THAT we keep His commandments; and His commandments are not burdensome.
THE Love that the Christian is supposed to demonstrate (live out) toward God is a love “THAT KEEPS His Commandments”- a love that does NOT think of God’s Commandments as “burdensome”… THIS is “Love” as GOD defines it!
And what about LOVE for your neighbor- “the new” (or fresh) commandment of Christ Jesus for us to live by?
The Apostles of The Lord define this love as well for us:
Romans 13:8-11 (NASB)
Owe nothing to anyone except TO LOVE one another; for he who loves his neighbor has fulfilled the law.
 For this, “You shall not commit adultery, You shall not murder, You shall not steal, You shall not covet,”…
– “THIS is the love of God, THAT we keep His commandments”
… and IF THERE IS ANY OTHER COMMANDMENT, it is summed up in this saying, “You shall LOVE YOUR NEIGHBOR AS YOURSELF.”
 LOVE DOES NO WRONG TO a neighbor; LOVE therefore IS THE FULFILLMENT OF THE LAW.
 AND THIS DO, knowing the time, that it is already the hour for you to awaken from sleep; for now salvation is nearer to us than when we believed.
Paul is in agreement then with what James says about The Faith that saves:
James 2:20 (NASB)
But are you willing to recognize, you foolish fellow, that faith without works is useless?
James 2:26 (NASB)
For just as the body without the spirit is dead, so also faith without works is dead.
Paul’s, “Faith which works by Love” IS the same as James’, “Faith was Working WITH his Works, AND as a result of The Works faith was perfected” (or made complete)
James 2:24 (KJV)
Ye see then how that by works a man is justified, and NOT BY FAITH ONLY.
Paul and James were in agreement then on this matter- since they both taught the same thing.
One taught “faith which works by love” (while pointing out that “love is the fulfilling of The Law”); the other taught Faith without works” (of obedience to The Law/Commandments) “is dead”, “useless”.
The Apostles were our Lord, Jesus’ chosen teachers for us (His students- His disciples):
Luke 6:13 (NASB)
And when day came, He called His disciples to Him; and chose twelve of them, whom He also named as apostles:
John 20:21 (KJV)
Then said Jesus to them again, Peace be unto you: as my Father hath sent me, even so send I you.
2 Peter 1:19 (NASB)
And so WE HAVE THE PROPHETIC WORD made more sure, TO WHICH YOU DO WELL TO PAY ATTENTION AS TO A LAMP shining in a dark place, until the day dawns and the morning star arises in your hearts.
John 17:17-20 (NASB)
“Sanctify them in THE TRUTH; THY WORD IS TRUTH.
 “As Thou didst send Me into the world, I also have sent them into the world.
 “And for their sakes I sanctify Myself, that they themselves also may be sanctified in truth.
 “I do not ask in behalf of these alone, BUT FOR THOSE ALSO WHO BELIEVE IN ME THROUGH THEIR WORD;  that they may all be one; even as Thou, Father, art in Me, and I in Thee, that they also may be in Us; that the world may believe that Thou didst send Me… …
… … …  I in them, and Thou in Me, that they may be perfected in unity, that the world may know that Thou didst send Me, and didst love them, even as Thou didst love Me.
As HIS chosen teachers, Jesus sent HIS Apostles for us (we who live today), to teach us about The Truth (God’s Word) through their writings in The Bible.
It is THESE chosen Apostles who have just taught us that we are to REPENT FROM (turn away from) the breaking The Commandments/Laws of God (“Sin”), when it comes to our daily living toward God and our neighbors in Christ Jesus.
When we turn to Jesus Christ through Faith in God having provided Him as our Savior, we are taught to STOP violating The Commandments of God in this life, and to turn to OBEY the Commandments of God.
Exodus 20:2-17 (KJV)
I am the Lord thy God, which have brought thee out of the land of Egypt, out of the house of bondage.
*  THOU SHALT HAVE NO OTHER GODS BEFORE ME.
*  THOU SHALT NOT MAKE UNTO THEE ANY GRAVEN IMAGE, or any likeness of any thing that is in heaven above, or that is in the earth beneath, or that is in the water under the earth:  THOU SHALT NOT BOW DOWN THYSELF TO THEM, NOR SERVE THEM: for I the Lord thy God am a jealous God, visiting the iniquity of the fathers upon the children unto the third and fourth generation of them that hate me;  And shewing mercy unto thousands of them that love me, AND KEEP MY COMMANDMENTS.
*  THOU SHALT NOT TAKE THE NAME OF THE LORD THY GOD IN VAIN; for the Lord will not hold him guiltless that taketh his name in vain.
*  REMEMBER THE SABBATH DAY, TO KEEP IT HOLY.  Six days shalt thou labour, and do all thy work:  But THE SEVENTH DAY IS THE SABBATH OF THE LORD thy God: in it thou shalt not do any work, thou, nor thy son, nor thy daughter, thy manservant, nor thy maidservant, nor thy cattle, nor thy stranger that is within thy gates:  For in six days the Lord made heaven and earth, the sea, and all that in them is, and rested THE SEVENTH DAY: wherefore THE LORD BLESSED THE SABBATH DAY, AND HALLOWED IT.
*  HONOUR THY FATHER AND THY MOTHER: that thy days may be long upon the land which the Lord thy God giveth thee.
*  THOU SHALT NOT KILL.
*  THOU SHALT NOT COMMIT ADULTERY.
*  THOU SHALT NOT STEAL.
*  THOU SHALT NOT BEAR FALSE WITNESS against thy neighbour.
*  THOU SHALT NOT COVET thy neighbour’s house, thou shalt not covet thy neighbour’s wife, nor his manservant, nor his maidservant, nor his ox, nor his ass, nor any thing that is thy neighbour’s.
The Answer to the question- Does The Law of God Apply to The Christian’s Life ? – YES, The Laws (the Commandments) of God do indeed apply to The Christian life!
The Christian (one baptized into “repentance from dead works”, “to serve the living God” IS EXPECTED TO LIVE THEIR LIFE (“that from henceforth we should not serve sin”) IN REPENTANCE FROM the lifestyle that violates The Law (The Commandments) of God (“Sin is the transgression of the law”).
Hebrews 6:1 (KJV)
Therefore leaving THE PRINCIPLES OF THE DOCTRINE OF CHRIST, LET US GO ON UNTO PERFECTION; not laying again THE FOUNDATION
– of REPENTANCE FROM DEAD WORKS,
– and of FAITH toward God,
–  of the doctrine of baptisms,
– and of laying on of hands,
– and of resurrection of the dead,
– and of eternal judgment.
And Once we have achieved THIS- “The Principles of The Doctrine of Christ” / “the foundation”– it is THEN that we will be equipped and fully able to “press on unto Perfection” (literally: maturity).
For related subjects- you may refer to the following studies:
– “What is The Gospel of Jesus Christ”
– “A Summary of What It Means To Be Christian– According to The Word of God”