The first Covenant with God was based on his people keeping the Law of God. Let us look at the New Covenant:
Jesus has now obtained a more excellent ministry, and to that degree he is the mediator of a better covenant, which has been enacted on the basis of better promises. For if that first covenant had been faultless, there would have been no need to look for a second one. (Hebrews 8:6-7)
The New Covenant was prophesied in the Old Testament:
Therefore say to the house of Israel: Thus says the Lord God: It is not for your sake, O house of Israel, that I am about to act but for the sake of my holy name, which you have profaned among the nations to which you came. will sanctify my great name, which has been profaned among the nations and which you have profaned among them, and the nations shall know that I am the Lord, says the Lord God, when through you I display my holiness before their eyes. I will take you from the nations and gather you from all the countries and bring you into your own land. I will sprinkle clean water upon you, and you shall be clean from all your uncleannesses, and from all your idols I will cleanse you. A new heart I will give you, and a new spirit I will put within you, and I will remove from your body the heart of stone and give you a heart of flesh. I will put my spirit within you and make you follow my statutes and be careful to observe my ordinances. Then you shall live in the land that I gave to your ancestors, and you shall be my people, and I will be your God. (Ezekiel 36:22-28)
The days are surely coming, says the Lord, when I will make a new covenant with the house of Israel and the house of Judah. It will not be like the covenant that I made with their ancestors when I took them by the hand to bring them out of the land of Egypt—a covenant that they broke, though I was their husband, says the Lord. But this is the covenant that I will make with the house of Israel after those days, says the Lord: I will put my law within them, and I will write it on their hearts, and I will be their God, and they shall be my people. No longer shall they teach one another or say to each other, “Know the Lord,” for they shall all know me, from the least of them to the greatest, says the Lord, for I will forgive their iniquity and remember their sin no more. (Jeremiah 31:31-34)
It is clear that the New Covenant is based on the grace of God alone. God did, through Christ, what the law could not enable man to do: he fulfilled the law’s requirement. This can be described in covenantal terms as Christ, being God’s agent, fulfilling those obligations that the Sinai covenant had laid upon God’s people.
“Do not think that I have come to abolish the Law or the Prophets; I have come not to abolish but to fulfill. For truly I tell you, until heaven and earth pass away, not one letter,[a] not one stroke of a letter, will pass from the law until all is accomplished. (Matthew 5:17-18)
The Apostle Paul wrote:
For Christ is the culmination of the law so that there may be righteousness for everyone who believes. (Romans 10)
Christ did what we all could not do. He lived a perfect life and did not sin. Not only that, but he paid the price for sin by his death on a cruel cross. How do we respond? Do we respond with faith. Paul continues:
But what does it say?
“The word is near you,
in your mouth and in your heart”
(that is, the word of faith that we proclaim), because if you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved. For one believes with the heart, leading to righteousness, and one confesses with the mouth, leading to salvation. The scripture says, “No one who believes[d] in him will be put to shame.” (Romans 10:8-11)
The New Covenant is not just a Church doctrine. It offers us freedom from the power of sin and glorification with Christ:
Therefore there is now no condemnation for those who are in Christ Jesus. For the law of the Spirit of life in Christ Jesus has set you free from the law of sin and of death. For God has done what the law, weakened by the flesh, could not do: by sending his own Son in the likeness of sinful flesh and to deal with sin, he condemned sin in the flesh, so that the just requirement of the law might be fulfilled in us, who walk not according to the flesh but according to the Spirit. For those who live according to the flesh set their minds on the things of the flesh, but those who live according to the Spirit set their minds on the things of the Spirit. To set the mind on the flesh is death, but to set the mind on the Spirit is life and peace. For this reason the mind that is set on the flesh is hostile to God; it does not submit to God’s law—indeed, it cannot, and those who are in the flesh cannot please God.
But you are not in the flesh; you are in the Spirit, since the Spirit of God dwells in you. Anyone who does not have the Spirit of Christ does not belong to him. But if Christ is in you, then the body is dead because of sin, but the Spirit is life because of righteousness. If the Spirit of him who raised Jesus from the dead dwells in you, he who raised Christ Jesus[j] from the dead will give life to your mortal bodies also through[k] his Spirit that dwells in you.
So then, brothers and sisters, we are obligated, not to the flesh, to live according to the flesh— for if you live according to the flesh, you will die, but if by the Spirit you put to death the deeds of the body, you will live. For all who are led by the Spirit of God are children of God. For you did not receive a spirit of slavery to fall back into fear, but you received a spirit of adoption. When we cry, “Abba! Father!” it is that very Spirit bearing witness with our spirit that we are children of God, and if children, then heirs: heirs of God and joint heirs with Christ, if we in fact suffer with him so that we may also be glorified with him. (Romans 8:1-17)