Azariah, the son of Zadok, the priest - "The priest" here belongs to Azariah, not to Zadok. The term used כהן kôhên means sometimes a priest, sometimes a civil officer, with perhaps a semi-priestly character. (See 2-Samuel 8:18 note.) In this place it has the definite article prefixed, and can only mean "the high priest." Azariah, called here the "son," but really the "grandson," of Zadok, seems to have succeeded him in the priesthood 1-Chronicles 6:10. His position as high priest at the time when this list was made out gives Azariah the foremost place in it.

These were the princes which he had; Azariah the son of Zadok the priest - These were his great, chief, or principal men. None of them were princes in the common acceptation of the word.

And these [were] the (a) princes which he had; (b) Azariah the son of Zadok the priest,
(a) That is, his chief officers.
(b) He was the son of Achimais and Zadok's nephew.

And these were the princes which he had,.... That were in office about him, in the highest posts of honour and trust:
Azariah the son of Zadok the priest: or rather his grandson, since Ahimaaz was the son of Zadok, and Azariah the son of Ahimaaz, 1-Chronicles 6:8; though another Zadok may be meant, and his son not a priest but a prince, as the word may be rendered, and was Solomon's prime minister of state, and the rather, since he is mentioned first.

these were the princes--or chief officers, as is evident from two of them marrying Solomon's daughters.
Azariah the son of Zadok the priest--rather, "the prince," as the Hebrew word frequently signifies (Genesis 41:45; Exodus 2:16; 2-Samuel 8:18); so that from the precedency given to his person in the list, he seems to have been prime minister, the highest in office next the king.

The first of the שׂרים, princes, i.e., chief ministers of state or dignitaries, mentioned here is not the commander-in-chief, as under the warlike reign of David (2-Samuel 8:16; 2-Samuel 20:23), but, in accordance with the peaceful rule of Solomon, the administrator of the kingdom (or prime minister): "Azariah the son of Zadok was הכּהן," i.e., not the priest, but the administrator of the kingdom, the representative of the king before the people; like כּהן in v. 5, where this word is interpreted by המּלך רעה, with this difference, however, arising from the article before כּהן, that Azariah was the Kohen par excellence, that is to say, held the first place among the confidential counsellors of the king, so that his dignity was such as befitted the office of an administrator of the kingdom. Compare the explanation of כּהן at 2-Samuel 8:18. The view of the Vulgate, Luther, and others, which has been revived by Thenius, namely, that כּהן is to be connected as a genitive with בּן־צדוק in opposition to the accents, "Azariah the son of Zadok the priest," is incorrect, and does not even yield any sense, since the connection of these words with the following Elichoreph, etc., is precluded by the absence of the copula Vav, which would be indispensable if Azariah had held the same office as the two brothers Elichoreph and Achijah.
(Note: The objection by which Thenius tries to set aside this argument, which has been already advanced by Houbigant, viz., that "if the first (Azariah) was not also a state scribe, the copula would be inserted, as it is everywhere else from v. 4 onwards when a new office is mentioned," proves nothing at all, because the copula is also omitted in v. 3, where the new office of מזכּיר is introduced.)
Moreover, Azariah the son of Zadok cannot be a grandson of Zadok the high priest, i.e., a son of Ahimaaz the son of Zadok, as many infer from 1 Chr. 5:34-35 (1-Chronicles 6:8-9); for, apart from the fact that Zadok's grandson can hardly have been old enough at the time for Solomon to invest him with the chief dignity in the kingdom, which would surely be conferred upon none but men of mature years, we can see no reason why the Azariah mentioned here should not be called the son of Ahimaaz. If the Zadok referred to here was the high priest of that name, Azariah can only have been a brother of Ahimaaz. And there is no real difficulty in the way, since the name Azariah occurs three times in the line of high priests (1 Chr. 5:36, 39), and therefore was by no means rare.

Princes - That is, the chief rulers or officers. The son - Or the grand - son. The priest - The second priest, or the priest that attended upon Solomon's person in holy offices and administrations.