Theophylact of Ohrid

Since, he says, He suffered, having offered Himself as a sacrifice, for this reason He was also "called... High Priest." Moreover, although He offered blood as a sacrifice, it was not according to the order of the Jewish high priests, but according to the order of Melchizedek. For just as that one was not anointed by man, so also Christ was not — but by God, through the Spirit consubstantial with Him. Just as that king did not offer the sacrifices required by the law, so also this One did not — and in countless other ways.

Commentary on Hebrews ↗

Oecumenius

"being designated by God a High Priest." And having been made perfect, he became the source of eternal salvation for all who obey him." Therefore, this is perfection in humans, that through sufferings they attain completeness. And He has said everything fitting for a human. "the source of eternal salvation."

The Pseudo-Oecumenian Catena on Hebrews ↗

Thomas Aquinas

261. – Therefore he says, being designated by God a high priest after the order of Melchizedech.

Commentary on Hebrews ↗