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?
And if the priesthood is changed, the law must also be changed to permit it.
For the priest we are talking about belongs to a different tribe, whose members have never served at the altar as priests. What I mean is, our Lord came from the tribe of Judah, and Moses never mentioned priests coming from that tribe.
This change has been made very clear since a different priest, who is like Melchizedek, has appeared. 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.
And the psalmist pointed this out when he prophesied, "You are a priest forever in the order of Melchizedek." Yes, the old requirement about the priesthood was set aside because it was weak and useless. - Hebrews 7:11-18 NLT
Set aside, ἀθέτησις: abolished, disannulled, put away, rejected, cancelled.
Replaced.
Hebrews 8:7 If the first covenant had been faultless, there would have been no need for a second covenant to replace it.
Made obsolete.
Hebrews 8:13 When God speaks of a "new" covenant, it means he has made the first one obsolete. It is now out of date and will soon disappear [as something that is decaying]
The Temple was still standing when this was written. Sacrifices were being offered. Circumcisions were being performed. Priests were being ordained. The old system was still visible, but it was lifeless, like an old shirt that was set aside never to be worn again.
And not just the part about priests, but the whole law, v 19...
...And the prophets, for Christ said not one jot or tittle shall pass from the law till all had been fulfilled.
Matthew 5:17-18 KJV Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil. For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, [the law will not change] till all be fulfilled.
But wait! What did Paul say?
if the priesthood is changed, the law must also be changed to permit it.
And if the law is changed even one jot, it means all has been fulfilled.

(Sorry, Dispensationalists. That's gotta hurt!)