When Jesus comes, He is introduced as “Jesus Christ the son of David, the son of Abraham” (Matthew 1:1). Here is David’s Seed who reigns eternally. Here is Abraham’s Seed who brings God’s blessing to all nations. Here also is the Prophet like Moses who speaks for God (Deuteronomy 18:15), the One to whom the Law and the Prophets point (Luke 24:44-47; Acts 3:18-26). Yes, here is the fulfillment of the covenants!
Jesus comes as a Jew under the law of Moses (Galatians 4:4). Jesus obeys that law and requires His fellow-Jews to obey it too (Matthew 5:17-19; 8:4; 23:23). But He also fulfills the prophecies of the coming of the New Covenant (Jeremiah 31:31- 32; Isaiah 42:6; 55:3; 61:8).
But as it is, Christ has obtained a ministry that is as much more excellent than the old as the covenant He mediates is better, since it is enacted on better promises. For if that first covenant had been faultless, there would have been no occasion to look for a second. For He finds fault with them when He says: “Behold, the days are coming, declares the Lord, when I will establish a new covenant with the house of Israel and with the house of Judah, not like the covenant that I made with their fathers on the day when I took them by the hand to bring them out of the land of Egypt. For they did not continue in My covenant, and so I showed no concern for them, declares the Lord.” (Hebrews 8:6-9)
Jesus is now the Mediator for the New Covenant. This New Covenant displaces the Old Covenant, as the same Scriptures make clear.
In speaking of a new covenant, He makes the first one obsolete. And what is becoming obsolete and growing old is ready to vanish away. (Hebrews 8:13)
[Jesus] added, “Behold, I have come to do Your will.” He does away with the first in order to establish the second. And by that will we have been sanctified through the offering of the body of Jesus Christ once for all. (Hebrews 10:9-10)