Hebrews 7:11

If, then, Perfection had been attainable through the Levitical priesthood--and it was under this priesthood that the people received the Law--why was it still necessary that a priest of a different order should appear, a priest of the order of Melchizedek and not of the order of Aaron?

Hebrews 8:7

If that first Covenant had been faultless, there would have been no occasion for a second.

Galatians 2:21

I do not reject the love of God. If righteousness comes through Law, then there was no need for Christ to die!

Hebrews 5:6

and on another occasion also-- 'Thou art a priest for all time of the order of Melchizedek.'

Hebrews 7:17-19

for that is the meaning of the declaration-- 'Thou art for all time a priest of the order of Melchizedek.'

Galatians 4:3

And so is it with us; when we were under age, as it were, we were slaves to the puerile teaching of this world;

Galatians 4:9

But now that you have found God--or, rather, have been found by him--how is it that you are turning back to that poor and feeble puerile teaching, to which yet once again you are wanting to become slaves?

Colossians 2:10-17

And, by your union with him, you also are filled with it. He is the Head of all Archangels and Powers of Heaven.

Hebrews 5:10

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

Hebrews 6:20

where Jesus, our Forerunner, has entered on our behalf, after being made for all time a High Priest of the order of Melchizedek.

Hebrews 7:15

All this becomes even yet plainer when we remember that a new priest has appeared, resembling Melchizedek,

Hebrews 7:21

but his appointment was ratified by an oath, when God said to him-- 'The Lord has sworn, and will not change, "Thou art a priest for all time."'

Hebrews 8:10-13

"This is the Covenant that I will make with the People of Israel After those days," says the Lord. "I will impress my laws on their minds, and will inscribe them on their hearts; And I will be their God, and they shall be my People.

Hebrews 10:1-4

The Law, though able to foreshadow the Better System which was coming, never had its actual substance. Its priests, with those sacrifices which they offer continuously year after year, can never make those who come to worship 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
On the one hand, we have the abolition of a previous regulation as being both inefficient and useless
Hebrews 8:7
If that first Covenant had been faultless, there would have been no occasion for a second.
Hebrews 10:1
The Law, though able to foreshadow the Better System which was coming, never had its actual substance. Its priests, with those sacrifices which they offer continuously year after year, can never make those who come to worship perfect.
Galatians 2:21
I do not reject the love of God. If righteousness comes through Law, then there was no need for Christ to die!
Galatians 4:3
And so is it with us; when we were under age, as it were, we were slaves to the puerile teaching of this world;
Colossians 2:10
And, by your union with him, you also are filled with it. He is the Head of all Archangels and Powers of Heaven.

What

Hebrews 7:26
This was the High Priest that we needed--holy, innocent, spotless, withdrawn from sinners, exalted above the highest Heaven,

Another

Hebrews 7:15
All this becomes even yet plainer when we remember that a new priest has appeared, resembling Melchizedek,
Hebrews 5:6
and on another occasion also-- 'Thou art a priest for all time of the order of Melchizedek.'
Hebrews 6:20
where Jesus, our Forerunner, has entered on our behalf, after being made for all time a High Priest of the order of Melchizedek.