John Chrysostom : What need was there then of another priesthood? "For the priesthood being changed, there is of necessity a change of the law also." But if there must be another priest, or rather another priesthood, there must needs be also another law. This is for those who say, What need was there of a new Covenant? For he could indeed have alleged a testimony from prophecy also. "This is the covenant which I made with your fathers." But for the present he contends on the ground of the priesthood. And observe, how he says this from the first. He said, "According to the order of Melchisedec." By this he excluded the order of Aaron. For he would not have said "After the order of Melchisedec," if the other had been better. If therefore another priesthood has been brought in, there must be also another Covenant; for neither is it possible that there should be a priest, without a covenant and laws and ordinances, nor that having received a different priesthood He should use the former covenant. — Homily on Hebrews 13 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? "For the priesthood being changed [or transferred]," from tribe to tribe, from the sacerdotal to the regal tribe, that the same might be both regal and sacerdotal. — Homily on Hebrews 13 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 introduced. — The Pseudo-Oecumenian Catena on Hebrews