Hebrews 7:11

Now if perfection had been reached through the Levitical priesthood -- for on it as a basis even the law was enacted for the people-- what further need would there have been of appointing a different priest, with the rank of Melchizedek, instead of designating one with the rank of Aaron?

Hebrews 8:7

For if the first covenant had been faultless, there could have been no room for a second one.

Galatians 2:21

I never can nullify the unmerited favor of God. For if right standing with God could come through law, then Christ died for nothing.

Hebrews 5:6

as also in another passage He says: "You are a priest forever, belonging to the rank of Melchizedek."

Hebrews 7:17-19

For the Scripture bears witness: "You are a priest forever, with the rank of Melchizedek."

Galatians 4:3

So when we were spiritually under age, we were slaves to the world's crude notions,

Galatians 4:9

but now, since you have come to know God, or rather have come to be known by Him, how can you turn back to your own crude notions, so weak and worthless, and wish to become slaves to them again?

Colossians 2:10-17

and through union with Him you too are filled with it. He is the Head of all principalities and dominions.

Hebrews 5:10

since He had received from God the title of a High Priest with the rank of Melchizedek.

Hebrews 6:20

(6:19) where Jesus has blazed the way for us and became a High Priest with the rank of Melchizedek.

Hebrews 7:15

And it is still more overwhelmingly clear, since a different priest in the likeness of Melchizedek is appointed,

Hebrews 7:21

for the Levitical priests were appointed without His taking an oath, but He with His oath, when He said to Him: "The Lord took oath and will not change, You are a priest forever" --

Hebrews 8:10-13

'For this is the covenant that I will make with the house of Israel in those days,' says the Lord; 'I will put my laws into their minds, and write them on their hearts, and I will be their God, and they will be my people. And nevermore will each one need to teach his fellow-citizen,

Hebrews 10:1-4

For since the law cast only a shadow of the blessings to come and did not possess the reality itself of those blessings, the priests with the same sacrifices that are perpetually offered year after year cannot make perfect those who come to worship.

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
Indeed, the rescinding of a previous regulation takes place, because it was weak and ineffective --
Hebrews 8:7
For if the first covenant had been faultless, there could have been no room for a second one.
Hebrews 10:1
For since the law cast only a shadow of the blessings to come and did not possess the reality itself of those blessings, the priests with the same sacrifices that are perpetually offered year after year cannot make perfect those who come to worship.
Galatians 2:21
I never can nullify the unmerited favor of God. For if right standing with God could come through law, then Christ died for nothing.
Galatians 4:3
So when we were spiritually under age, we were slaves to the world's crude notions,
Colossians 2:10
and through union with Him you too are filled with it. He is the Head of all principalities and dominions.

What

Hebrews 7:26
For we needed such a High Priest, holy, innocent, unstained, far removed from sinful men, and elevated far above the very heavens,

Another

Hebrews 7:15
And it is still more overwhelmingly clear, since a different priest in the likeness of Melchizedek is appointed,
Hebrews 5:6
as also in another passage He says: "You are a priest forever, belonging to the rank of Melchizedek."
Hebrews 6:20
(6:19) where Jesus has blazed the way for us and became a High Priest with the rank of Melchizedek.