Albert Barnes Commentary Hebrews 7:21

"(for they indeed have been made priests without an oath; but he with an oath by him that saith of him, The Lord sware and will not repent himself, Thou art a priest for ever);" — Hebrews 7:21 (ASV)

For those priests were made without an oath. The Levitical priests were set apart and consecrated without their office being confirmed to them by an oath from God. They received it by regular descent, and when they arrived at a suitable age, they entered on it as a matter of course. Jesus received his office by special appointment, and it was secured to him by an oath. The word rendered "oath" is, in the margin, "swearing of an oath." This is the proper meaning of the Greek word, but the meaning is not significantly changed.

But this with an oath. This priest, the Lord Jesus, became a priest by means of an oath.

The Lord sware. (See Barnes on Hebrews 6:3).

The reference here is to Psalm 110:4: The Lord hath sworn, and will not repent. This means He will not regret, or will not change His mind because of regret—for this is the meaning of the Greek word.