Albert Barnes Commentary 1 Kings 4:2

"And these were the princes whom he had: Azariah the son of Zadok, the priest;" — 1 Kings 4:2 (ASV)

Azariah, the son of Zadok, the priest - The title “the priest” here belongs to Azariah, not to Zadok. The Hebrew term used, כהן (kôhên), can mean either a priest or a civil officer with a semi-priestly character (see the note on 2 Samuel 8:18). In this instance, however, the term has the definite article prefixed, which means it can only be translated as “the high priest.”

Azariah, who is called the “son” but was actually the “grandson” of Zadok, appears to have succeeded him in the priesthood (1 Chronicles 6:10). His position as high priest at the time this list was compiled gives Azariah the foremost place in it.