Hebrews 7:11

Now if the crowning blessing was attainable by means of the Levitical priesthood--for as resting on this foundation the people received the Law, to which they are still subject-- what further need was there for a Priest of a different kind to be raised up belonging to the order of Melchizedek instead of being said to belong to the order of Aaron?

Hebrews 8:7

For if that first Covenant had been free from imperfection, there would have been no attempt to introduce another.

Galatians 2:21

I do not nullify the grace of God; for if acquittal from guilt is obtainable through the Law, then Christ has died in vain."

Hebrews 5:6

as also in another passage He says, "Thou art a priest for ever, belonging to the order of Melchizedek."

Hebrews 7:17-19

For the words are in evidence, "Thou art a priest for ever, belonging to the order of Melchizedek."

Galatians 4:3

So we also, when spiritually we were children, were subject to the world's rudimentary notions, and were enslaved.

Galatians 4:9

Now, however, having come to know God--or rather to be known by Him--how is it you are again turning back to weak and worthless rudimentary notions to which you are once more willing to be enslaved?

Colossians 2:10-17

and He is the Lord of all princes and rulers.

Hebrews 5:10

For God Himself addresses Him as a High Priest for ever, belonging to the order of Melchizedek.

Hebrews 6:20

where Jesus has entered as a forerunner on our behalf, having become, like Melchizedek, a High Priest for ever.

Hebrews 7:15

And this is still more abundantly clear when we read that it is as belonging to the order of Melchizedek that a priest of a different kind is to arise,

Hebrews 7:21

for these men hold office without any oath having been taken, but He holds it attested by an oath from Him who said to Him, "The Lord has sworn and will not recall His words, Thou art a Priest for ever" --

Hebrews 8:10-13

But this is the Covenant that I will covenant with the house of Israel after those days,' says the Lord: I will put My laws into their minds and will write them upon their hearts. And I will indeed be their God and they shall be My People.

Hebrews 10:1-4

For, since the Law exhibits only an outline of the blessings to come and not a perfect representation of the things themselves, the priests can never, by repeating the same sacrifices which they continually offer year after year, give complete freedom from sin to 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?

Bible References

Perfection

Hebrews 7:18
On the one hand we have here the abrogation of an earlier code because it was weak and ineffective--
Hebrews 8:7
For if that first Covenant had been free from imperfection, there would have been no attempt to introduce another.
Hebrews 10:1
For, since the Law exhibits only an outline of the blessings to come and not a perfect representation of the things themselves, the priests can never, by repeating the same sacrifices which they continually offer year after year, give complete freedom from sin to those who draw near.
Galatians 2:21
I do not nullify the grace of God; for if acquittal from guilt is obtainable through the Law, then Christ has died in vain."
Galatians 4:3
So we also, when spiritually we were children, were subject to the world's rudimentary notions, and were enslaved.
Colossians 2:10
and He is the Lord of all princes and rulers.

What

Hebrews 7:26
Moreover we needed just such a High Priest as this--holy, guileless, undefiled, far removed from sinful men and exalted above the heavens;

Another

Hebrews 7:15
And this is still more abundantly clear when we read that it is as belonging to the order of Melchizedek that a priest of a different kind is to arise,
Hebrews 5:6
as also in another passage He says, "Thou art a priest for ever, belonging to the order of Melchizedek."
Hebrews 6:20
where Jesus has entered as a forerunner on our behalf, having become, like Melchizedek, a High Priest for ever.