Hebrews 7:11

If therefore perfection were by the Levitical priesthood,
&c.] The priesthood which was established in the tribe of Levi; so called, to distinguish it from that which was before this institution, from the times of Adam, as well as from the priesthood of Melchizedek, and from the priesthood of Christ, and from that of his people under the Gospel, who are all priests; as well as to restrain it to the subject of the apostle's discourse: the design of which is to show, that there is no perfection by it; as is clear from the priests themselves, who were but men, mortal men, sinful men, and so imperfect, and consequently their priesthood; and from their offerings, between which, and sin, there is no proportion; and at best were but typical of the sacrifice of Christ; and could neither make the priests nor the worshippers perfect, neither in their own consciences, nor in the sight of God: moral actions are preferred before them, and yet by these there is no perfection, justification, and salvation; to which may be added, that the sacrifices the priests offered did not extend to all kind of sins, only to sins of ignorance, not to presumptuous ones; and there were many under that dispensation punished with death; and at most they only delivered from temporal, not eternal punishment, and only entitled to a temporal life, not an eternal one.

For under it the people received the law:
not the moral law, which was given to Adam in innocence, and as it came by Moses, it was before the Levitical priesthood took place; but the ceremonial law, and which was carnal, mutable, and made nothing perfect: the Syriac version renders it, "by which a law was imposed upon the people"; to regard the office of priesthood, and the priests in it, and bring their sacrifices to them; and the Arabic version reads, "the law of a the priest's office"; which office was after the law of a carnal commandment, and so imperfect, as is manifest from what follows: for had perfection been by it,

what further need was there that another priest should arise
after the order of Melchisedec, and not be called after the order
of Aaron?
that there was another priest promised and expected, and that he should arise after the order of Melchizedek, and who was to make his soul an offering for sin, is certain, ( Ezra 2:63 ) ( Psalms 110:4 ) ( Isaiah 53:10 ) and such an one is risen, even Jesus of Nazareth; and yet there would have been no need of him, and especially that he should be of a different order from Aaron's, had there been perfection by the Levitical priesthood.