11 So if the priesthood of Levi, on which the law was based, could have achieved the perfection God intended, why did God need to establish a different priesthood, with a priest in the order of Melchizedek instead of the order of Levi and Aaron? 12 And if the priesthood is changed, the law must also be changed to permit it. 13 For the priest we are talking about belongs to a different tribe, whose members have never served at the altar as priests. 14 What I mean is, our Lord came from the tribe of Judah, and Moses never mentioned priests coming from that tribe. 15 This change has been made very clear since a different priest, who is like Melchizedek, has appeared. 16 Jesus became a priest, not by meeting the physical requirement of belonging to the tribe of Levi, but by the power of a life that cannot be destroyed. 17 And the psalmist pointed this out when he prophesied, "You are a priest forever in the order of Melchizedek."
Matthew Henry's Commentary on Hebrews 7:11-17
Commentary on Hebrews 7:11-25
(Read Hebrews 7:11-25)
The priesthood and law by which perfection could not come, are done away; a Priest is risen, and a dispensation now set up, by which true believers may be made perfect. That there is such a change is plain. The law which made the Levitical priesthood, showed that the priests were frail, dying creatures, not able to save their own lives, much less could they save the souls of those who came to them. But the High Priest of our profession holds his office by the power of endless life in himself; not only to keep himself alive, but to give spiritual and eternal life to all who rely upon his sacrifice and intercession. The better covenant, of which Jesus was the Surety, is not here contrasted with the covenant of works, by which every transgressor is shut up under the curse. It is distinguished from the Sinai covenant with Israel, and the legal dispensation under which the church so long remained. The better covenant brought the church and every believer into clearer light, more perfect liberty, and more abundant privileges. In the order of Aaron there was a multitude of priests, of high priests one after another; but in the priesthood of Christ there is only one and the same. This is the believer's safety and happiness, that this everlasting High Priest is able to save to the uttermost, in all times, in all cases. Surely then it becomes us to desire a spirituality and holiness, as much beyond those of the Old Testament believers, as our advantages exceed theirs.