Hebrews 7:11

Thus if perfection was through the Levitical priesthood, for on the basis of it the people received the law, what further need [is there] for another priest to arise according to the order of Melchizedek and not said to be according to the order of Aaron?

Hebrews 8:7

For if that first [covenant] had been faultless, occasion would not have been sought for a second.

Galatians 2:21

I do not declare invalid the grace of God, for if righteousness [is] through the law, then Christ died to no purpose.

Hebrews 5:6

just as also in another [place] he says, "You [are] a priest {forever} according to the order of Melchizedek,"

Hebrews 7:17-19

For it is testified, "You [are] a priest {forever} according to the order of Melchizedek."

Galatians 4:3

So also we, when we were children, we were enslaved under the elemental spirits of the world.

Galatians 4:9

But now, [because you] have come to know God, or rather have come to be known by God, how can you turn back again to the weak and miserable elemental spirits? Do you want to be enslaved to them all over again?

Colossians 2:10-17

and you are filled in him, who is the head over every ruler and authority,

Hebrews 5:10

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

Hebrews 6:20

where Jesus, the forerunner for us, entered, [because he] became a high priest {forever} according to the order of Melchizedek.

Hebrews 7:15

And it is still more clear, if another priest according to the likeness of Melchizedek arises,

Hebrews 7:21

but he with an oath by 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 decree with the house of Israel after those days, says the Lord: I am putting my laws in their minds and I will write them on their hearts, and I will be {their} God and they will be {my} people.

Hebrews 10:1-4

For the law, possessing a shadow of the good [things] that are about to come, not the form of things itself, [is] never able {year by year} by means of the same sacrifices which they offer without interruption to 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 a preceding commandment is set aside because of its weakness and uselessness
Hebrews 8:7
For if that first [covenant] had been faultless, occasion would not have been sought for a second.
Hebrews 10:1
For the law, possessing a shadow of the good [things] that are about to come, not the form of things itself, [is] never able {year by year} by means of the same sacrifices which they offer without interruption to make perfect those who draw near.
Galatians 2:21
I do not declare invalid the grace of God, for if righteousness [is] through the law, then Christ died to no purpose.
Galatians 4:3
So also we, when we were children, we were enslaved under the elemental spirits of the world.
Colossians 2:10
and you are filled in him, who is the head over every ruler and authority,

What

Hebrews 7:26
For a high priest such as this indeed is fitting for us, holy, innocent, undefiled, separated from sinners, and having become exalted [above] the heavens,

Another

Hebrews 7:15
And it is still more clear, if another priest according to the likeness of Melchizedek arises,
Hebrews 5:6
just as also in another [place] he says, "You [are] a priest {forever} according to the order of Melchizedek,"
Hebrews 6:20
where Jesus, the forerunner for us, entered, [because he] became a high priest {forever} according to the order of Melchizedek.

General references

Numbers 20:26
Strip off Aaron's garments, and put them on Eleazar his son; Aaron will be gathered [to his people], and he will die there."