Hebrews 7:11

Further, if the Levitical priesthood had been the means of reaching perfection (for it was on the basis of that priesthood that the Law was enacted for the People), why was it still necessary for another sort of priest to emerge with the rank of Melchizedek, instead of simply with the rank of Aaron

Hebrews 8:7

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

Galatians 2:21

I do not annul God's grace; but if righteousness comes by way of the Law, then indeed Christ's death was useless.

Hebrews 5:6

Just as elsewhere he says, Thou art a priest for ever, with the rank of Melchizedek.

Hebrews 7:17-19

for the witness to him is, Thou art priest for ever, with the rank of Melchizedek.

Galatians 4:3

So with us. When we were under age, we lived under the thraldom of the Elemental spirits of the world;

Galatians 4:9

but now that you know God ??or rather, are known by God ??how is it you are turning back again to the weakness and poverty of the Elemental spirits? Why do you want to be enslaved all over again by them?

Colossians 2:10-17

it is in him that you reach your full life, and he is the Head of every angelic Ruler and Power;

Hebrews 5:10

being designated by God high priest with the rank of Melchizedek.

Hebrews 6:20

There Jesus entered for us in advance, when he became high priest for ever with the rank of Melchizedek.

Hebrews 7:15

This becomes all the more plain when another priest emerges resembling Melchizedek,

Hebrews 7:21

Previous priests became priests apart from any oath, but he has an oath from Him who said to him, The Lord has sworn, and he will not change his mind, thou art a priest for ever.

Hebrews 8:10-13

This is the covenant I will make with the house of Israel when that day comes, saith the Lord; I will set my laws within their mind, inscribing them upon their hearts; I will be a God to them, and they shall be a People to me;

Hebrews 10:1-4

For as the Law has a mere shadow of the bliss that is to be, instead of representing the reality of that bliss, it never can perfect those who draw near with the same annual sacrifices that are perpetually offered.

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
A previous command is set aside on account of its weakness and uselessness
Hebrews 8:7
For if the first covenant had been faultless, there would have been no occasion for a second.
Hebrews 10:1
For as the Law has a mere shadow of the bliss that is to be, instead of representing the reality of that bliss, it never can perfect those who draw near with the same annual sacrifices that are perpetually offered.
Galatians 2:21
I do not annul God's grace; but if righteousness comes by way of the Law, then indeed Christ's death was useless.
Galatians 4:3
So with us. When we were under age, we lived under the thraldom of the Elemental spirits of the world;
Colossians 2:10
it is in him that you reach your full life, and he is the Head of every angelic Ruler and Power;

What

Hebrews 7:26
Such was the high priest for us, saintly, innocent, unstained, lifted high above the heavens, far from all contact with the sinful,

Another

Hebrews 7:15
This becomes all the more plain when another priest emerges resembling Melchizedek,
Hebrews 5:6
Just as elsewhere he says, Thou art a priest for ever, with the rank of Melchizedek.
Hebrews 6:20
There Jesus entered for us in advance, when he became high priest for ever with the rank of Melchizedek.