John Chrysostom

Then also there are other points: He is made Priest (he says) by Another and does not of Himself intrude into the office. This too is common, "And no man taketh this honor to himself, but he that is called of God as was Aaron." Here again he conciliates them in another point, because He was sent from God: which Christ was wont to say throughout to the Jews. …

Homily on Hebrews 8 ↗

Theophylact of Ohrid

He points out another distinguishing mark of the high priest, which is also revealed in Christ — that He did not assume the priesthood by Himself, but that He was called by God and thus received it. Here he also hints at the Jewish high priests of that time, who sought the office by purchasing it and violating the law. For Aaron too, having first been called by God through Moses, served as priest in this way, not having seized this dignity for himself. …

Commentary on Hebrews ↗

Oecumenius

"To offer for sins."The sacrifice concerning sins, he says, "And no one takes this honor upon himself." He speaks of another characteristic of a priest, that he does not take it upon himself to approach the honor of the priesthood. This he also hinted at when he spoke of the priests of the Jews at that time, who were not priests by power, because they approached and had made the priesthood a service. "just as Aaron." For Aaron was often appointed high priest by God. …

The Pseudo-Oecumenian Catena on Hebrews ↗

Thomas Aquinas

249. – Then he describes how one goes about attaining to the priesthood when he says, And one does not take the honor upon himself. For it is contrary to nature for anything to raise itself to a higher state than its nature, as air does not make itself fire, but is made so by something higher. …

Commentary on Hebrews ↗