Hebrews 7:11

So, if perfection [i.e., a right relationship with God] could have been attained through the Levitical priesthood, (for under it people had received the law of Moses), what further need would there have been for another priest to arise, according to the order of Melchizedek, who was not considered "according to the order of Aaron"?

Hebrews 8:7

For if that first Agreement had been faultless, then there would have been no need for a second one.

Galatians 2:21

[In doing this] I am not trying to disregard God's unearned favor, for if a person could become right with God by [perfect obedience to the requirements of] the law of Moses, then Christ died for nothing.

Hebrews 5:6

And He says in another place [Psa. 110:4], "You are a priest forever according to the order of Melchizedek." [Note: This is the first mention of this mysterious Old Testament priest who, throughout this book, is represented as a type of Christ].

Hebrews 7:17-19

For it is declared [about Jesus in the Scriptures, Psa. 110:4], "You are a priest forever according to the order of Melchizedek."

Galatians 4:3

So also, when we [Jews] were like children, we were under bondage to the basic worldly rules [of the law of Moses].

Galatians 4:9

But now that you have come to know God [as your Father], or rather, to be known by Him [as His children], how can you turn back again to the weak, cheap, elementary teachings [of the law of Moses], to which you [seem to] desire to become enslaved?

Colossians 2:10-17

and you people have been made full [i.e., spiritually complete] in [fellowship with] Him, who is the [spiritual] head over all who rule and have authority.

Hebrews 5:10

[So], God declared Him to be a Head Priest according to the order of Melchizedek.

Hebrews 6:20

where Jesus, our forerunner, [already] entered on our behalf, having become a Head Priest forever according to the order of Melchizedek.

Hebrews 7:15

And this is even clearer if another priest like Melchizedek arises,

Hebrews 7:21

(for [Levitical] priests were appointed without [God] taking [such] an oath, but Christ was appointed with an oath by God when He said to Him [Psa. 110:4], "The Lord made a vow and will not change His mind [when He said], 'You are a priest forever')."

Hebrews 8:10-13

For this is the Agreement that I will make with the people of Israel in the coming days, says the Lord: I will put my laws into their minds, and I will also write them on their hearts. And I will be their God and they will be my people.

Hebrews 10:1-4

For the law of Moses was [only] a foreshadow of the good things that [were] to come [i.e., in the Messianic age], not the exact image of those things. It can never, by the same sacrifices, continually offered year after year, make [morally] perfect those who draw near [to God in 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
For on one hand, the previous command [i.e., the law of Moses] was set aside because it was weak and useless,
Hebrews 8:7
For if that first Agreement had been faultless, then there would have been no need for a second one.
Hebrews 10:1
For the law of Moses was [only] a foreshadow of the good things that [were] to come [i.e., in the Messianic age], not the exact image of those things. It can never, by the same sacrifices, continually offered year after year, make [morally] perfect those who draw near [to God in worship].
Galatians 2:21
[In doing this] I am not trying to disregard God's unearned favor, for if a person could become right with God by [perfect obedience to the requirements of] the law of Moses, then Christ died for nothing.
Galatians 4:3
So also, when we [Jews] were like children, we were under bondage to the basic worldly rules [of the law of Moses].
Colossians 2:10
and you people have been made full [i.e., spiritually complete] in [fellowship with] Him, who is the [spiritual] head over all who rule and have authority.

What

Hebrews 7:26
For Jesus was a very suitable head priest for us [i.e., He meets our needs very well], because He was holy, innocent, without [moral] corruption, separated from sinners and [exalted] above the heavens.

Another

Hebrews 7:15
And this is even clearer if another priest like Melchizedek arises,
Hebrews 5:6
And He says in another place [Psa. 110:4], "You are a priest forever according to the order of Melchizedek." [Note: This is the first mention of this mysterious Old Testament priest who, throughout this book, is represented as a type of Christ].
Hebrews 6:20
where Jesus, our forerunner, [already] entered on our behalf, having become a Head Priest forever according to the order of Melchizedek.