Hebrews 7:11

Now if there were perfection through the Levitical priesthood, (and it was under it that the people received the Law) why was it still necessary for another kind of priest to arise, after the order of Melchizedek, instead of being reckoned according to the order of Aaron?

Hebrews 8:7

For if the first covenant had been faultless, there would have been no need for a second.

Galatians 2:21

I do not annul the grace of God; for if righteousness comes by way of the Law, then indeed Christ died Christ for nothing.

Hebrews 5:6

and again, Thou art a priest forever, after the order of Melchizedek.

Hebrews 7:17-19

For the words are in evidence, Thou art a priest forever after the order of Melchizedek.

Galatians 4:3

So we Jews also, when we were children, were held in bondage under the empty externalities of the world.

Galatians 4:9

Now, however, when you have come to know God, or rather to be known by God, how is it that you are beginning to turn back to those weak and beggarly externalities, eager to be in bondage to them again?

Colossians 2:10-17

and in him you have your fulness, and he is the Lord of all the principalities and powers.

Hebrews 5:10

while God himself pronounced him High Priest according to the order of Melchizedek.

Hebrews 6:20

whither Jesus himself is entered as a forerunner on our behalf, having become a priest forever, after the order of Melchizedek.

Hebrews 7:15

And this is yet more abundantly clear if, after the likeness of Melchizedek, there arises another Priest,

Hebrews 7:21

For although those priests became such without an oath, He had an oath form God who said to him, The Lord hath sworn and will not change, Thou art a priest forever.

Hebrews 8:10-13

"For this is the covenant which I will covenant with the house of Israel, After these days," says the Lord; "I will put my laws into their minds, And upon their hearts will I write them; And I will be their God, And they shall be my people;

Hebrews 10:1-4

For the Law, being only a shadow of the good things to come, and not their very substance, its priests cannot with the same sacrifice which year after year they offer continually, 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?

Bible References

Perfection

Hebrews 7:18
For there is a setting aside of a foregoing commandment, because of its weakness and unprofitableness
Hebrews 8:7
For if the first covenant had been faultless, there would have been no need for a second.
Hebrews 10:1
For the Law, being only a shadow of the good things to come, and not their very substance, its priests cannot with the same sacrifice which year after year they offer continually, make perfect those who draw near.
Galatians 2:21
I do not annul the grace of God; for if righteousness comes by way of the Law, then indeed Christ died Christ for nothing.
Galatians 4:3
So we Jews also, when we were children, were held in bondage under the empty externalities of the world.
Colossians 2:10
and in him you have your fulness, and he is the Lord of all the principalities and powers.

What

Hebrews 7:26
For we needed just such a high priest, holy, innocent, undefiled, separated from sinners, and exalted above the heavens;

Another

Hebrews 7:15
And this is yet more abundantly clear if, after the likeness of Melchizedek, there arises another Priest,
Hebrews 5:6
and again, Thou art a priest forever, after the order of Melchizedek.
Hebrews 6:20
whither Jesus himself is entered as a forerunner on our behalf, having become a priest forever, after the order of Melchizedek.