Covenant of Grace is not a Biblical expression. It is used by some to describe the New Covenant in Christ. God made a Covenant with Israel at Sinai; but Israel failed to keep it.
God promised a New Covenant.
Jeremiah 31:31-34 Behold, the days come, saith the LORD, that I will make a new covenant with the house of Israel, and with the house of Judah: 32 Not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt; which my covenant they brake, although I was an husband unto them, saith the LORD: 33 But this shall be the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people. 34 And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.
Jesus Christ fulfilled the Old Covenant and established the New Covenant.
Hebrews 8:8 For finding fault with them, he saith, Behold, the days come, saith the Lord, when I will make a new covenant with the house of Israel and with the house of Judah:
Hebrews 8:13 In that he saith, A new covenant, he hath made the first old. Now that which decayeth and waxeth old is ready to vanish away.
Jesus Christ is the mediator of the New Covenant.
Hebrews 12:24 And to Jesus the mediator of the new covenant, and to the blood of sprinkling, that speaketh better things than that of Abel.
Matthew 26:28 NKJV "For this is My blood of the new covenant, which is shed for many for the remission of sins.
Under the Old Covenant, eternal life was promised to those who kept the Law perfectly.
Leviticus 18:5 Ye shall therefore keep my statutes, and my judgments: which if a man do, he shall live in them: I am the LORD.
Galatians 3:12 And the law is not of faith: but, The man that doeth them shall live in them.
Only Jesus Christ kept it, everyone else is condemned to death by it.
Romans 7:10 And the commandment, which was ordained to life, I found to be unto death.
Under the New Covenant, eternal life is promised to those who believe and obey the gospel of Jesus Christ.
To be part of the New Covenant in Christ we must:
1. Understand and believe the gospel preached by Jesus Christ.
Mark 16:15-16 And he said unto them, Go ye into all the world, and preach the gospel to every creature. 16 He that believeth and is baptized shall be saved; but he that believeth not shall be damned (condemned).
2. Repent of our sinful way of life and be baptised by immersion in water for the remission of our past sins.
Acts 2:38 …Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins…
3. Live a new life by obeying Jesus’ commandments.
Romans 6:4 Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life.
John 14:21 He that hath my commandments, and keepeth them, he it is that loveth me:
Luke 6:46 And why call ye me, Lord, Lord, and do not the things which I say?
4. After baptism we will still sin, but providing we are making a determined effort to live by Christ’s commandments, our sins will be forgiven by confession in prayer.
1 John 1:7-9 … if we walk in the light, as he is in the light, we have fellowship one with another, and the blood of Jesus Christ his Son cleanseth us from all sin. 8 If we say that we have no sin, we deceive ourselves, and the truth is not in us. 9 If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness.
5. Hold fast to the gospel to the end of our lives.
Matthew 10:22… he that endureth to the end shall be saved.
Salvation in Christ is by faith, demonstrated by works of faith.Faith without works is dead.
James 2:14 What doth it profit, my brethren, though a man say he hath faith, and have not works? can faith save him?
James 2:20 But wilt thou know, O vain man, that faith without works is dead?
The sacrifice of Christ is efficacious for men and women of faith of all generations.
Romans 1:17 For therein is the righteousness of God revealed from faith to faith: as it is written, The just shall live by faith.
Romans 3:30 Seeing it is one God, which shall justify the circumcision by faith, and uncircumcision through faith.
In the day of Judgment when Christ returns to raise the dead, faith will be counted for righteousness.
Romans 4:5 But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness.
This is called salvation by Grace because it is a free gift of God which is not earned by the works of the Law.
Romans 6:23 For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.
Romans 4:16 Therefore it is of faith, that it might be by grace; to the end the promise might be sure to all the seed; not to that only which is of the law, but to that also which is of the faith of Abraham; who is the father of us all,
Ephesians 2:8 For by grace are ye saved through faith; and that not of yourselves: it is the gift of God:
Thus, the New Covenant in Jesus Christ, is termed by some the Covenant of Grace.
Some erroneously teach that Grace is a supernatural gift given to believers to prevent them sinning. In truth it is the favour of God whereby he is willing to forgive the sins of those under the New Covenant.
Hebrews 4:16 Let us therefore come boldly unto the throne of grace, that we may obtain mercy, and find grace to help in time of need.
I hope you find this helpful.