The New Covenant is defined as
a covenant between God and his people that is anticipated in the Old Testament (Jer 31:31) and fulfilled in the New Testament (Luke 22:20; 1 Cor 11:25; Heb 9:15; 12:24). The new covenant involves forgiveness of sin, spiritual transformation, and the fulfillment of God’s promises to Israel.
Before going further into this covenant, I want to review some of what has lead up to this New Covenant: The unconditional Abrahamic Covenant was the first major covenant. It promised land, seed and blessings. In addition, it had conditional blessings. To enjoy the blessings of the Abrahamic Covenant, Israel needed to be obedient to the laws of God recorded in the Mosaic Covenant, which was given in conjunction with the Abrahamic Covenant. History records Israel was incapable to achieve the obedience required of the Mosaic Covenant. As a result, Israel could not experience the blessings. The only way to have the blessings was forgiveness for sins, a new heart of obedience and enablement from God. Thus, enters the assurance of these supplies from the New Covenant in Jeremiah 31:31-34.
“Behold, days are coming,” declares the Lord, “when I will make a new covenant with the house of Israel and with the house of Judah, not like the covenant which I made with their fathers in the day I took them by the hand to bring them out of the land of Egypt, My covenant which they broke, although I was a husband to them,” declares the Lord. “But this is the covenant which I will make with the house of Israel after those days,” declares the Lord, “I will put My law within them and on their heart I will write it; and I will be their God, and they shall be My people. “They will not teach again, each man his neighbor and each man his brother, saying, ‘Know the Lord,’ for they will all know Me, from the least of them to the greatest of them,” declares the Lord, “for I will forgive their iniquity, and their sin I will remember no more.” (Jeremiah 31:31–34, NASB95)
The definition above and Jeremiah 31:31-34 describe almost exactly what Pentecost states is needed for Israel. This context can be summarized this way: “God’s New Covenant will give Israel the inner ability to obey His righteous standards and thus to enjoy His blessings.” The New Covenant is then further established in Jeremiah 32:37-42, Ezekiel 16:60-62 and 36:24-32.
This covenant directly relates to the Abrahamic Covenant because of the original promises of land, seed, and blessings given. Again, the Davidic Covenant advances the seed promises, and now the New Covenant advances and assures the blessing promises of the Abrahamic Covenant. This New Covenant assures the conservation of Israel as a nation and ultimate restoration to the land originally given through the Abrahamic Covenant (Jeremiah 31:38-40). In addition,
It provides for a new mind so the nation may know God, and for a new heart so that those in the nation may love God. It promises the indwelling of the Holy Spirit who will enable them to walk in obedience to the demands of God. And as a result of this covenant, the blessings Israel never found through the Law [Mosaic Covenant] will at last be experienced.
 Abner Chou, “New Covenant,” ed. John D. Barry et al., The Lexham Bible Dictionary (Bellingham, WA: Lexham Press, 2016).
 J. Dwight Pentecost, Thy Kingdom Come: Tracing God’s Kingdom Program and Covenant Promises Throughout History (Grand Rapids: Kregel Publications, 1995), 164.
 Charles H. Dyer, “Jeremiah,” in The Bible Knowledge Commentary An Exposition of the Scriptures by Dallas Seminary Faculty 2 Volumes Old & New Testament, ed. J. F. Walvoord and R. B. Zuck, vol. 1 (Wheaton, IL: Victor Books, 1985), 1171.
 J. Dwight Pentecost, Thy Kingdom Come: Tracing God’s Kingdom Program and Covenant Promises Throughout History (Grand Rapids: Kregel Publications, 1995), 171.