Hebrews 7:11

Now if it was possible for things to be made complete through the priests of the house of Levi (for the law was given to the people in connection with them), what need was there for another priest who was of the order of Melchizedek and not of the order of Aaron?

Hebrews 8:7

For if that first agreement had been as good as possible, there would have been no place for a second.

Galatians 2:21

I do not make the grace of God of no effect: because if righteousness is through the law, then Christ was put to death for nothing.

Hebrews 5:6

As he says in another place, You are a priest for ever after the order of Melchizedek.

Hebrews 7:17-19

For it has been witnessed of him, You are a priest for ever after the order of Melchizedek.

Galatians 4:3

So we, when we were young, were kept under the first rules of the world;

Galatians 4:9

But now that you have come to have knowledge of God, or more truly, God has knowledge of you, how is it that you go back again to the poor and feeble first things, desiring to be servants to them again?

Colossians 2:10-17

And you are complete in him, who is the head of all rule and authority:

Hebrews 5:10

Being named by God a high priest of the order of Melchizedek.

Hebrews 6:20

Where Jesus has gone before us, as a high priest for ever after the order of Melchizedek.

Hebrews 7:15

And this is even more clear if a second priest has come up who is like Melchizedek,

Hebrews 7:21

(For those were made priests without an oath, but this one was made a priest with an oath by him who says of him, The Lord gave his oath, which he will not take back, that you are a priest for ever);

Hebrews 8:10-13

For this is the agreement which I will make with the people of Israel after those days: I will put my laws into their minds, writing them in their hearts: and I will be their God, and they will be my people:

Hebrews 10:1-4

For the law, being only a poor copy of the future good things, and not the true image of those things, is never able to make the people who come to the altar every year with the same offerings completely clean.

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
So the law which went before is put on one side, because it was feeble and without profit.
Hebrews 8:7
For if that first agreement had been as good as possible, there would have been no place for a second.
Hebrews 10:1
For the law, being only a poor copy of the future good things, and not the true image of those things, is never able to make the people who come to the altar every year with the same offerings completely clean.
Galatians 2:21
I do not make the grace of God of no effect: because if righteousness is through the law, then Christ was put to death for nothing.
Galatians 4:3
So we, when we were young, were kept under the first rules of the world;
Colossians 2:10
And you are complete in him, who is the head of all rule and authority:

What

Hebrews 7:26
It was right for us to have such a high priest, one who is holy and without evil, doing no wrong, having no part with sinners, and made higher than the heavens:

Another

Hebrews 7:15
And this is even more clear if a second priest has come up who is like Melchizedek,
Hebrews 5:6
As he says in another place, You are a priest for ever after the order of Melchizedek.
Hebrews 6:20
Where Jesus has gone before us, as a high priest for ever after the order of Melchizedek.

General references

Numbers 20:26
And take Aaron's robes off him and put them on Eleazar, his son: and death will come to Aaron there, and he will be put to rest with his people.

Basic English, produced by Mr C. K. Ogden of the Orthological Institute - public domain