Matthew Poole and continuators on Hebrews 7:11

11 If therefore perfection were by the Levitical priesthood (for under it the people received the law ) what further need was there that another priest should arise after the order of Melchisedec, and not be called after the order of Aaron?

Now the Spirit infers from the Doctrine of Melchisedec's Priesthood, the dignity and perpetuity of Christ's typified by it. So that it is not Aaron's Priesthood, but Christ's which the Hebrews were to use for their Salvation after Aaron's was expired. For Perfection was not to be had by Aaron's Priesthood or Law, but by a better, of another Order, even Christ and his Law. The form of these words are interrogative, implying a vehement denial of what is queried in them. A perfecting of Persons to Life eternal by Expiation, Justification, Renovation, &c. See ch. 9.9. and 10.1. freeing Sinners from the Guilt, Stain, Filth, and Consequents of their Sins by an explatory satisfactory Sacrifice to God, and fitting of them for an eternal enjoying him: A Self-efficiency to these things without Christ, is as to the Aaronical Priesthood vehehemently denied; as to this, that is defective.

For with the Priesthood, about the time of its Institution by God, the Israelitish Church, God's covenanted People, received the Law; by which, as well as by its Priesthood, there is no Expiation, Remission, nor eternal Life to be obtained, Gal. 3.17, 18, 19. comp. Mal. 2.4, to 8. This Law and Priesthood being Types of far better to succeed them, they were but leading to them, which in the fulness of Time were to be revealed, and which should perfect what they could not, Gal. 3.23, 24. and 4.3, 4, 5.

It was needful since the Levitical Priesthood and Law could not perfect Sinners, that another should take place which could perfect them. David therefore, who lived above 400 years after their Institution, and feeling their Imperfection, did by the Spirit fore-see and tell of a Royal Priesthood and Law to take place after this, that should perfect Sinners, which could not be done by any called after Aaron's imperfect Order. This was the Lord Christ the Messiah, who must be after the Order of Melchisedec▪ Psalm 110.4. and who by his Priesthood and Law should abundantly effect it; which was far more excellent for both, than any of the Levitical Family can pretend to.

Marginal references: Gal. 2.21. v. 18, 19.