Greg Nichols’ Covenant Theology states something very interesting.
“God’s covenant with David is unique. It crowns the Mosaic economy and organically binds it to the Christian economy (Jer 33:15,17). God’s covenant with Jesus, David’s heir, fulfills the Davidic covenant."
He expands this and concludes at the end,
"God fulfills his redemptive favor to his people in the Christian economy. It is the ultimate set of God’s covenants with his people. He makes the Messianic covenant with Jesus and the new covenant with his people, Jesus’ posterity, through the mediation of Jesus. In this mediation Christ evangelically reforms and spiritually transforms God’s people. The Abrahamic also provides the framework for this Messianic transformation. By gospel transformation Christ spiritually transforms God’s people from Hebrew Israel under the old covenant to Christian Israel under the new."