It is quite correct to think of the Old Testament as promise (of the Messiah) and the New Testament as fulfillment (Messiah’s coming). At the end of the OT, Malachi had foretold the coming of Elijah, who would “turn the hearts of fathers to their children and the hearts of children to their fathers” (Malachi 4:6). Jesus identified himself as the fulfillment of that and many other OT prophecies. Matthew immediately begins with “The book of the genealogy of Jesus Christ, the son of David, the son of Abraham” (1:1).
Not only does Matthew reach back into the genealogy to explain who Jesus is, when the angel spoke to Joseph about Mary giving birth to a son by the Holy Spirit, he clarified: “All this took place to fulfill what the Lord had spoken by the prophet” (1:22). Matthew goes on to quote Isaiah. From the beginning, God had set his redemptive plan into place and, step by step, he has worked it out, “the mystery hidden for ages and generations but now revealed to his saints” (Colossians 1:26). We are the glad recipients of that good news!
Come, thou long expected Jesus,
born to set thy people free;
from our fears and sins release us,
let us find our rest in thee.
Israel's strength and consolation,
hope of all the earth thou art;
dear desire of every nation,
joy of every longing heart. –Charles Wesley