God appoints prophets to judge and guide Israel, and those prophets anoint Israel's leaders.  In the Old Testament, then, authority passes from God to the prophets, who speak on God's behalf, and from the prophets to the king and civil rulers, whom the prophets identify and anoint.

Christ founds a new Israel, the Church, as is clear from his calling of the Twelve, to stand in the place of the Twelve Tribes of ancient times.  In the old Israel, God makes covenants with David, the king, and intervenes through the prophetic office in the appointment of a chief steward, as we see in Isaiah.  In the new Israel, the king is Christ, who appoints Peter as his chief steward to keep the keys of the kingdom.  The Apostles, who hold the prophetic office and are given the Holy Spirit, are empowered to anoint leaders in the new Israel, like Isaiah did, and to pass on the Holy Spirit to their successors, as Elijah did to Elisha.

In the new Israel, it is true, their is "no king but Christ," but if we accept Christ as the perfection of the Davidic kingship, then we must also expect that the other elements of the Israel of the Old Covenant are perfected in the New.