John Chrysostom

"As He saith also in another place, Thou art a Priest forever after the order of Melchisedech." Unto whom now was this spoken? Who is "after the order of Melchisedech"? No other than He. For they all were under the Law, they all kept sabbaths, they all were circumcised; one could not point out any other than Him.

Homily on Hebrews 8 ↗

Oecumenius

The meaning of the word is that if Christ himself did not offer an unbloody sacrifice (for he offered his own body), then those priests who are deemed worthy by God and the high priest will offer an unbloody sacrifice from him. For this indicates, "forever." For he would not have said "forever" regarding the one-time sacrifice and offering made by God, but he refers to the present priests through whom Christ ministers and is ministered to, having also given them in the mystical supper the manner of such ministry.

The Pseudo-Oecumenian Catena on Hebrews ↗

Thomas Aquinas

As man He also receives the high priesthood from God: as he says also in another place: 'You are a priest for ever according to the order of Melchizedech'. But the Apostle uses the authority of the Psalms as being more famous and more often consulted. He says, priest, because He offered Himself to God the Father: 'He loved us and gave himself for us an oblation and offering to God' (Eph. 5:2). …

Commentary on Hebrews ↗