John Calvin Commentary Hebrews 7:11

"Now if there was perfection through the Levitical priesthood (for under it hath the people received the law), what further need [was there] that another priest should arise after the order of Melchizedek, and not be reckoned after the order of Aaron?" — Hebrews 7:11 (ASV)

If therefore perfection, or, moreover, if perfection, and so forth. From this same testimony, the Apostle concludes that the old covenant was abrogated by the coming of Christ. He has until now spoken of the office and person of the priest. But since God had instituted a priesthood for the purpose of ratifying the Law, the priesthood being abolished, the Law necessarily ceases.

So that this may be better understood, we must keep in mind the general truth—that no covenant between God and humanity is in force and ratified unless it rests on a priesthood. Therefore, the Apostle says that the Law was introduced among the ancient people under the Levitical priesthood. By this, he intimates that it not only prevailed during the time of the Law but, as we have said, was also instituted for the sake of confirming the Law.

He now reasons as follows: If the ministry of the Church under the order of Aaron was perfect, why was it necessary to turn to another order? For in perfection, nothing can be changed. It then follows that the ministry of the Law was not perfect, because that new order, of which David speaks, was to be introduced.

The scriptural phrase, For under it the people received the Law, and so on. This parenthesis is inserted so that we may know that the Law was annexed to the priesthood. The Apostle intended to prove that in the Law of Moses there was no ultimate end at which we ought to stop.

This he proves by the abrogation of the priesthoods, and in this way: Had the authority of the ancient priesthood been such as to be sufficient to fully establish the Law, God would never have introduced in its place another and a different priesthood. Now, since some might doubt whether the abolition of the Law followed the abolition of the priesthood, he says that the Law was not only introduced under it but was also established by it.