Hebrews 7:11

If indeed perfection had been by the Levitical priesthood, (for under it the people hath received the Law,) what further need was there that a different priest should arise after the order of Melchizedek, and not be called alter the order of Aaron?

Hebrews 8:7

For if that first covenant had been faultless, then a place would not have been sought for a second.

Galatians 2:21

I do not set aside the grace of God; for if righteousness come through the Law, then did Christ die for nought.

Hebrews 5:6

as also he saith in another place, "Thou art a priest for ever, after the order of Melchizedek."

Hebrews 7:17-19

For it is testified of him, "Thou art a priest for ever, after the order of Melchizedek."

Galatians 4:3

So also we, when we were children, were in bondage under the rudiments of the world;

Galatians 4:9

but now, after having known God, or rather having been known by God, how is it that ye are turning back to the weak and beggarly rudiments to which ye wish to be again in bondage?

Colossians 2:10-17

and ye are made full in him, who is the head of all principality and power;

Hebrews 5:10

being addressed by God as highpriest after the order of Melchizedek.

Hebrews 6:20

where as forerunner for us Jesus entered, having become a highpriest for ever, after the order of Melchizedek.

Hebrews 7:15

And it is still more abundantly evident, if after the likeness of Melchizedek there ariseth a different priest,

Hebrews 7:21

for they indeed have been made priests without an oath; but he with an oath by him who said to him, "The Lord swore, and will not repent, Thou art a priest for ever,"

Hebrews 8:10-13

For this is the covenant that I will make with the house of Israel after those days, saith the Lord: I will put my laws into their mind, and on their hearts will I write them; and I will be to them a God, and they shall be to me a people.

Hebrews 10:1-4

For the Law but shadowing forth the good things to come, and not having the very image of the things, can never with the same sacrifices which they offer year by year continually make those who come with them perfect.

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 on the one hand there takes place an annulling of the commandment which went before, on account of its weakness and unprofitableness,
Hebrews 8:7
For if that first covenant had been faultless, then a place would not have been sought for a second.
Hebrews 10:1
For the Law but shadowing forth the good things to come, and not having the very image of the things, can never with the same sacrifices which they offer year by year continually make those who come with them perfect.
Galatians 2:21
I do not set aside the grace of God; for if righteousness come through the Law, then did Christ die for nought.
Galatians 4:3
So also we, when we were children, were in bondage under the rudiments of the world;
Colossians 2:10
and ye are made full in him, who is the head of all principality and power;

What

Hebrews 7:26
For such a highpriest also became us, holy, harmless, undefiled, separate from sinners, and made higher than the heavens;

Another

Hebrews 7:15
And it is still more abundantly evident, if after the likeness of Melchizedek there ariseth a different priest,
Hebrews 5:6
as also he saith in another place, "Thou art a priest for ever, after the order of Melchizedek."
Hebrews 6:20
where as forerunner for us Jesus entered, having become a highpriest for ever, after the order of Melchizedek.