Albert Barnes Commentary Psalms 110:4

"Jehovah hath sworn, and will not repent: Thou art a priest for ever After the order of Melchizedek." — Psalms 110:4 (ASV)

The Lord hath sworn - He has confirmed the appointment of the Messiah by a solemn oath, or as by an oath. That is, it is as sure and fixed as if he had taken an oath. . The “time,” so to speak, if the word time can be applied to transactions in a past eternity, was that when he was designated in the divine purpose as Messiah; in the eternal counsels of God. .

And will not repent - Will not change his purpose.

Thou art a priest forever after the order of Melchizedek - The word rendered “order” here means properly a word, a thing, a matter; hence, a way or manner. The meaning here is, that he would be a priest “after the manner” of Melchizedek; or, such a priest as he was. He would not be of the tribe of Levi; he would not be in the regular line of the priesthood, but he would resemble, in the characteristics of his office, this ancient priest-king, combining in himself the two functions of priest and king; as a priest, standing alone; not deriving his authority from any line of predecessors; and having no successors. See this verse explained at length, in its application to the Messiah, in the notes at Hebrews 5:6 (note), Hebrews 5:10 (note), and Hebrews 7:1-3 (note).

The passage as it stands here, and as looked at without any reference to the use made of it in the New Testament, would imply these things:

1. That he who was spoken of would be, in a proper sense, a priest.
2. That he would have a perpetual or permanent priesthood - “forever.”
3. That he would not be of the established line of priests in the tribe of Levi, but that his appointment would be unusual and extraordinary.
4. That the appointment would come directly from God, and would not be “derived” from those who went before him.
5. That as a priest he would “resemble” Melchizedek, according to the record which was found of Melchizedek in Genesis.
6. That as Melchizedek was a priest of the Most High God, so he would be.
7. That as Melchizedek combined in himself the functions of both priest and king, so these would be found in him.
8. That as Melchizedek had no successors in office, so he would have none.

How far these things were applicable to the Lord Jesus Christ, and with what propriety the passage might be applied to him, may be seen by examining the Epistle to the Hebrews, Hebrews 5–7.