Hebrews 7:11

If, therefore, there was perfection through the Levitical priesthood (for under it the people have received the law), what further need was there, that another Priest should arise according to the rank of Melchizedek, and not be reckoned according to the rank of Aaron?

Hebrews 8:7

For, if that first covenant had been faultless, place would not be sought for a second;

Galatians 2:21

I do not set aside the grace of God; for, if righteousness is through law, then Christ died needlessly!

Hebrews 5:6

as also, in another place, He saith, "Thou art a Priest forever according to the rank of Melchizedek";

Hebrews 7:17-19

for it is testified of Him, "Thou art a Priest forever according to the rank of Melchizedek."

Galatians 4:3

So we also, when we were children, were held in bondage under the elements of the world.

Galatians 4:9

but, after having known God, or rather having been known by God, how are ye turning back again to the weak and beggarly elements, to which ye desire to be in bondage again?

Colossians 2:10-17

and ye have been made complete in Him, Who is the Head of all principality and power;

Hebrews 5:10

having been addressed by God as "High Priest according to the rank of Melchizedek."

Hebrews 6:20

where, as Forerunner in our behalf, Jesus entered, having become a High Priest forever, according to the rank of Melchizedek.

Hebrews 7:15

And it is yet far more evident; if, according to the likeness of Melchizedek, there arises another Priest,

Hebrews 7:21

(for they, indeed, have been made priests without an oath; but He with an oath through Him Who said to Him, "The Lord swore, and will not repent, Thou art a Priest forever");

Hebrews 8:10-13

Because this is the covenant which I will make with the house of Israel after those days, saith the Lord: Putting My laws into their mind, I will also write them upon their hearts, and I will be to them a God, and they shall be to Me a people;

Hebrews 10:1-4

For the law, having a shadow of the good things to come, not the very likeness of the things, can never, with the same sacrifices, which they offer year by year continually, perfect those who come to them;

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?

Bible References

Perfection

Hebrews 7:18
For there is verily an annulling of a previous commandment, on account of its weakness and unprofitableness
Hebrews 8:7
For, if that first covenant had been faultless, place would not be sought for a second;
Hebrews 10:1
For the law, having a shadow of the good things to come, not the very likeness of the things, can never, with the same sacrifices, which they offer year by year continually, perfect those who come to them;
Galatians 2:21
I do not set aside the grace of God; for, if righteousness is through law, then Christ died needlessly!
Galatians 4:3
So we also, when we were children, were held in bondage under the elements of the world.
Colossians 2:10
and ye have been made complete in Him, Who is the Head of all principality and power;

What

Hebrews 7:26
For such a High Priest was befitting us, holy, harmless, undefiled, separated from sinners, and made higher than the heavens;

Another

Hebrews 7:15
And it is yet far more evident; if, according to the likeness of Melchizedek, there arises another Priest,
Hebrews 5:6
as also, in another place, He saith, "Thou art a Priest forever according to the rank of Melchizedek";
Hebrews 6:20
where, as Forerunner in our behalf, Jesus entered, having become a High Priest forever, according to the rank of Melchizedek.