Charles Ellicott Commentary 1 Kings 1:34

"and let Zadok the priest and Nathan the prophet anoint him there king over Israel; and blow ye the trumpet, and say, [Long] live king Solomon." — 1 Kings 1:34 (ASV)

Anoint him ... king.—It is notable that of this solemn inauguration of royalty, marked emphatically as a religious consecration by the common phrase “the Lord’s anointed”—at that time especially in use (1 Samuel 16:6; 1 Samuel 24:6; 1 Samuel 26:9; 2 Samuel 1:14; 2 Samuel 19:21), though found also occasionally in the later books (Lamentations 4:20)—there is no mention of the tumultuous usurpation of Adonijah.

Probably, as in the appointment of Saul and David himself, the right to anoint was recognised as belonging to the prophetic order (see 1 Kings 19:16), because it signified the outpouring of the Holy Spirit of the Lord . Hence, in the absence of Nathan, it could not be attempted. In the case of David, such anointing had marked (1 Samuel 16:13) his first private designation for the kingdom by Samuel, and his public accession to royalty, first over Judah (2 Samuel 2:4), then over all Israel (2 Samuel 5:3).

The completeness of the old King’s provision is especially to be noticed. The “riding on the King’s mule,” attended by the body-guard, marked the royal sanction; the anointing, the sanction of priest and prophet; and the acclamation the adhesion of the people. The enthronement and homage are then to follow.