The Old Covenant was made with Israel at Sinai and includes the ten commandments written on two stone tablets. Israel failed to keep the Covenant and so God promised a New Covenant.
Jeremiah 31:31 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.
The writer to the Hebrews explains:
Hebrews 8:6 But now hath he (Jesus Christ) obtained a more excellent ministry, by how much also he is the mediator of a better covenant, which was established upon better promises. 7 For if that first covenant had been faultless, then should no place have been sought for the second. 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: 9 Not according to the covenant that I made with their fathers in the day when I took them by the hand to lead them out of the land of Egypt; because they continued not in my covenant, and I regarded them not, saith the Lord. 10 For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people: 11 And they shall not teach every man his neighbour, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest. 12 For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more.
The New Covenant replaces the Old
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.
Jesus fulfilled the Old Covenant and took it out of the way when he died.
Jesus’ sacrifice ensured that the end clause of the New Covenant ‘I will forgive their iniquity’ was brought into force. Only in him can iniquities be forgiven.
To come into the New Covenant, we must:
1. Understand and believe the Gospel of the Kingdom of God.
Mark 16:15 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.
Acts 3:19 Repent ye therefore, and be converted, that your sins may be blotted out…
3. Be baptised by immersion in water into Christ for the remission of past sins.
Acts 2:38… be baptized every one of you in the name of Jesus Christ for the remission of sins…
4. Live a new life by the commandments of Jesus Christ.
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 15:14 Ye are my friends, if ye do whatsoever I command you.
Luke 6:46 And why call ye me, Lord, Lord, and do not the things which I say?
After baptism we will still sin, for we cannot live a sinless life. But providing we are making a determined effort to live by the commandments of Jesus Christ our sins will be forgiven by confession in prayer.
1 John 1:7… 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.
The commandments of Jesus Christ replace the Law of Moses under the New Covenant.
In Christ our faith will be counted for righteousness and our reward will be eternal life in the kingdom of God on earth when Jesus returns.
May I suggest that you read:
Your Share in God's Promises: https://www.thisisyourbible.com/library/show/181
I hope you find this helpful.