Albert Barnes 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 - Inauguration into each of the three offices (those of prophet, priest, and king) typical of the Messiah or Anointed One, was by anointing with oil. Divine appointment had already instituted the rite in connection with the kingly office (2 Samuel 2:4); however, after Solomon we have no express mention of the anointing of kings, except in the three cases of Jehu, Joash, and Jehoahaz, who were all appointed irregularly (2 Kings 9:6; 2 Kings 11:12; 2 Kings 23:30). At the time of the captivity, kings whose anointing has not been recorded in the historical books still bear the title of “the anointed of the Lord” (Lamentations 4:20; Psalms 89:38, 51).