Hebrews 7:11

Now if perfection was through the Levitical priesthood (for on the basis of it the people received the Law), what further need was there for another priest to arise according to the order of Melchizedek, and not be designated according to the order of Aaron?

Hebrews 8:7

For if that first covenant had been faultless, there would have been no occasion sought for a second.

Galatians 2:21

I do not nullify the grace of God, for if righteousness comes through the Law, then Christ died needlessly.”

Hebrews 5:6

just as He says also in another passage,
You are a priest forever
According to the order of Melchizedek.”

Hebrews 7:17-19

For it is attested of Him,
You are a priest forever
According to the order of Melchizedek.”

Galatians 4:3

So also we, while we were children, were held in bondage under the elemental things of the world.

Galatians 4:9

But now that you have come to know God, or rather to be known by God, how is it that you turn back again to the weak and worthless elemental things, to which you desire to be enslaved all over again?

Colossians 2:10-17

and in Him you have been made complete, and He is the head over all rule and authority;

Hebrews 5:10

being designated by God as a high priest according to the order of Melchizedek.

Hebrews 6:20

where Jesus has entered as a forerunner for us, having become a high priest forever according to the order of Melchizedek.

Hebrews 7:15

And this is clearer still, if another priest arises according to the likeness of Melchizedek,

Hebrews 7:21

(for they indeed became priests without an oath, but He with an oath through the One who said to Him,
The Lord has sworn
And will not change His mind,
You are a priest forever’”);

Hebrews 8:10-13

For this is the covenant that I will make with the house of Israel
After those days, says the Lord:
I will put My laws into their minds,
And I will write them on their hearts.
And I will be their God,
And they shall be My people.

Hebrews 10:1-4

For the Law, since it has only a shadow of the good things to come and not the very form of things, can never, by the same sacrifices which they offer continually year by year, make perfect those who draw near.

Treasury of Scripture Knowledge

Summary

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 rise after the order of Melchisedec, and not be called after the order of Aaron?

General references

Bible References

Perfection

Hebrews 7:18
For, on the one hand, there is a setting aside of a former commandment because of its weakness and uselessness
Hebrews 8:7
For if that first covenant had been faultless, there would have been no occasion sought for a second.
Hebrews 10:1
For the Law, since it has only a shadow of the good things to come and not the very form of things, can never, by the same sacrifices which they offer continually year by year, make perfect those who draw near.
Galatians 2:21
I do not nullify the grace of God, for if righteousness comes through the Law, then Christ died needlessly.”
Galatians 4:3
So also we, while we were children, were held in bondage under the elemental things of the world.
Colossians 2:10
and in Him you have been made complete, and He is the head over all rule and authority;

What

Hebrews 7:26
For it was fitting for us to have such a high priest, holy, innocent, undefiled, separated from sinners and exalted above the heavens;

Another

Hebrews 7:15
And this is clearer still, if another priest arises according to the likeness of Melchizedek,
Hebrews 5:6
just as He says also in another passage,
You are a priest forever
According to the order of Melchizedek.”
Hebrews 6:20
where Jesus has entered as a forerunner for us, having become a high priest forever according to the order of Melchizedek.

General references

Numbers 20:26
and strip Aaron of his garments and put them on his son Eleazar. So Aaron will be gathered to his people, and will die there.”