"11 Now if perfection had been attainable through the Levitical priesthood (for under it the people received the law), what further need would there have been for another priest to arise after the order of Melchizedek, rather than one named after the order of Aaron? 12 For when there is a change in the priesthood, there is necessarily a change in the law as well. 13 For the one of whom these things are spoken belonged to another tribe, from which no one has ever served at the altar.14 For it is evident that our Lord was descended from Judah, and in connection with that tribe Moses said nothing about priests.
15 This becomes even more evident when another priest arises in the likeness of Melchizedek, 16 who has become a priest, not on the basis of a legal requirement concerning bodily descent, but by the power of an indestructible life. 17 For it is witnessed of him,
“You are a priest forever,
after the order of Melchizedek.”
18 For on the one hand, a former commandment is set aside because of its weakness and uselessness 19 (for the law made nothing perfect); but on the other hand, a better hope is introduced, through which we draw near to God."
Hebrews 7:11-19
'Perfection' in 11 means 'achieving its desired and intentional end'. If in fact the Levitical priesthood had been able to effect what it in fact only illustrated and foreshadowed - namely, bringing men nigh to God (19) - there would obviously have been no need of any other priesthood to take its place. And the fact that David (in Psalm 110) speaks of another that would, in the fulness of time, supervene is ample proof of the weakness and unprofitableness of the old order (18). But to change the priesthood implies and involves a change of the whole constitution, so to speak. It is this that leads to the thought of a new covenant being instituted, and this the Apostle comes to in 22 and elaborates later in the epistle (ch 8). It might help us, in this closely reasoned and intricate argument, to think of Paul's teaching about the law in Romans 8 and Galatians 3. In Romans 8:3 he speaks of 'what the law could not do in that it was weak through the flesh', and this is certainly the point here, although our writer is thinking more in terms of the old system as a whole. The 'better hope' in 19 corresponds to 'God sending His own Son in the likeness of sinful flesh and for sin' (Romans 8:3) - and this was effectual in bringing men to God. It is of this that the contrast between Aaron and Melchizedek speaks, for the one priesthood was after the law of a carnal commandment, that is, owing its existence to a system of earthbound rules (NEB) or by virtue of a command imposed from outside, but the other, after the power of an endless life, a life that cannot be destroyed, is a reference to Christ's risen and exalted life at the right hand of God. His is therefore an eternal, unchanging Priesthood, by virtue of which, as we shall see in 25, He is able to save to the uttermost them that come unto God by Him.