John Chrysostom

In the next place, as to the ground of objection: "How could He be a priest if He were not a Levite?" Having overthrown this by what had been said above, he does not even think it worth answering, but introduces it in passing. I said (he means) that the priesthood was changed, therefore also the Covenant is. And it was changed not only in its character, or in its ordinances, but also in its tribe. For of necessity it must be changed in its tribe also. How? …

Homily on Hebrews 13 ↗

Theophylact of Ohrid

Now he shows how the law is gradually abolished, and in its place another covenant is introduced. For if the priesthood is changed, then it is necessary that the law also be different, for a priest does not exist without a covenant and laws and ordinances. The priesthood was changed not only in form, that is, so that it was not after the order of Aaron, but after the order of Melchizedek, but also in tribe. For it passed from the priestly tribe of Aaron to the royal tribe of Judah. Pay attention to the mystery. …

Commentary on Hebrews ↗

Oecumenius

"For the priesthood being changed." See how skillfully he introduces the new covenant. Whenever, he says, there has been a change of the priesthood, so that it is no longer according to the order of Aaron, but a priest arises according to the order of Melchizedek, and no longer from the lineage of Levi but from the lineage of Judah (for from this lineage Christ became a priest according to the flesh), it is necessary, he says, for the law and the covenant to be changed, that is, to be altered, and for another newer one to be …

The Pseudo-Oecumenian Catena on Hebrews ↗

Thomas Aquinas

350. – The second consequent is that it also does away with the Law which was administered by it. He states this when he says, When there is a change in the priesthood, there is necessarily a change in the law as well. For the Law was under the administration of the priesthood; therefore, the priesthood being translated, it is necessary that the Law be changed; just as a person who changes his mind about traveling by water, changes his mind about finding a ship. But every Law is ordained to leading one's life according to some rule. …

Commentary on Hebrews ↗