“In the Old Testament none of the covenant mediators– whether Adam, Noah, Abraham, Moses, or David– fulfilled their role and brought about the promise; they only typified and anticipated the one to come (Rom 5:14). Only our Lord Jesus Christ, the God-man, fulfills the roles of the previous covenantal mediators and brings about the promises stretching back to Gen 3:15.
That is why the New Testament presents Christ as nothing less than the Lord as well as the last Adam, the true seed of Abraham, David’s greater Son, who ushers in a new covenant– a covenant which all the previous covenants anticipated and typified. In Christ, all the promises of God are yes and amen (2 Cor 1:20).
That is why in Jesus and His cross work, the desperate plight begun in Eden now finds its solution as the last Adam, the obedient Son, has accomplished His saving work. The promise that God Himself must be the Savior of His people is fulfilled for He Himself is the Lord. Indeed, the death of Jesus, the crime of all crimes, is nevertheless determined by the divine plan (Acts 2:23).
Why? To bring to fulfillment what God had promised through the prophets, that the Messiah would suffer (Acts 3:18) in order to save His people from their sins (Matt 1:21). In Jesus Christ, the prophetic anticipation of God’s coming to save in and through David’s greater Son is fulfilled.”
–Stephen J. Wellum, “Baptism and the Relationships Between the Covenants,” in Believer’s Baptism: Sign of the New Covenant in Christ, Eds. Thomas Schreiner and Shawn Wright (Nashville: B&H, 2006), 131-132.