This is a helpful explanation from Tom Schreiner, and an encouragement to read his little book on the covenants.
Adam and Eve were called as priest-kings and as those made in the image of God to rule the world as God’s vice-regents. They were to do so under God’s lordship, but they rebelled against God and brought misery and death instead. God promised to reclaim the world through a child of Abraham. Through Abraham’s offspring there would be worldwide blessing, and God would rule in the land of Canaan.
When we come to the covenant with David, Israel was living under the Sinai covenant and hoping in the promises made to Abraham. King David and his sons would represent Israel, and the nation would be blessed through their obedience to Yahweh and their reign over the people. Their righteous rule would display to the world what it meant to live in the land under Yahweh. Hence, the covenant with David would bring about the promised blessings anticipated in the creation covenant, and the blessings promised in the covenants with Israel and Abraham would be realized.
Schreiner, Thomas R.. Covenant and God’s Purpose for the World (Short Studies in Biblical Theology) (p. 73). Crossway. Kindle Edition.