If perfection could have been attained through the Levitical priesthood—and indeed the law given to the people established that priesthood—why was there still need for another priest to come, one in the order of Melchizedek, not in the order of Aaron?  For when the priesthood is changed, the law must be changed also. He of whom these things are said belonged to a different tribe, and no one from that tribe has ever served at the altar. For it is clear that our Lord descended from Judah, and in regard to that tribe Moses said nothing about priests. 

Hebrews 7:11-14

In the last section, we got into the whole Melchizedek issue, and here, the author is applying it to our present situation in Christ.  A careful reading of this text will begin to reveal an amazing aspect of the relationship between the Old and New Covenants, and we quickly discover why the Old Covenant is no more.  To begin, verse 11 brings us a rhetorical question: If perfection could have been attained through the old priesthood, why do we need another?  Simple enough… Let’s understand “perfection” for a minute here, since I think it might refer to something that many might not be thinking about right off.  By “perfection” the author isn’t asking whether or not the Law could make a man perfect through His obedience to it; I’m sure you can recall Paul asking those kinds of questions.  In this case, perfection is linked to the priesthood itself, and the priesthood represents the entire Old Covenant system of atonement for sins.  Since that system cannot take sin away, it cannot bring about perfection. Jesus not only provided for forgiveness of sins, He took them away entirely.

Verse 12 brings up an interesting point in claiming that if the priesthood is changed, the Law must also be changed.  This is because the Levitical priesthood (Order of Aaron) was created and established by the Law, and a new priesthood can only be established by doing something with the Law first.  In the next verse, the author points out that the new high priest is from the tribe of Judah, and the old priests were from the tribe of Levi. According to the old Law, priests can only come from the tribe of Levi, while kings come from the tribe of Judah. Jesus came from Judah, the tribe of kings, and He was the heir to the throne of David. He is not eligible for priesthood under the Law of Moses… so something must give!

And what we have said is even more clear if another priest like Melchizedek appears, one who has become a priest not on the basis of a regulation as to his ancestry but on the basis of the power of an indestructible life.

Hebrews 7:15-16

Enter Melchizedek; he is a priest, but he is not a Levite, so how can he become a priest?  Think carefully now… a Levite is a priest because of a life force, in their case one of genetics and ancestry, but that life force is temporary, because they will die and need to pass the priestly office on to an heir.  Contrast this with the life force by which Melchizedek is made a priest: Indestructible life.  Which is better?

 For it is declared:

“You are a priest forever,
    in the order of Melchizedek.”

The former regulation is set aside because it was weak and useless (for the law made nothing perfect), and a better hope is introduced, by which we draw near to God.

Hebrews 7:17-19

Again we have the quote from Psalm 110:4. Melchizedek is priest forever; indestructible life. In addition the old Law was set aside because it was “weak and useless”.  An interesting note here is that the term “set aside” is a legal term.  Even now, when a judge sets something aside, he rules that it is null and void, and has no effect.

When the author says that the “law made nothing perfect” you might well notice that the Law is being spoken of in the past tense because it is entirely over.  Also, notice that “perfect” is being used in a different context than it was several verses back when it was applied only to the priesthood.  Here we are talking about the entire context of the Law, not just atonement.  Not only could the Law not take sin away, it made sin more evident than having no Law at all.  For anyone who cares to notice, the Law makes imperfection obvious, so that we can easily see that Man is quite lost without a direct relationship with God. Melchizedek’s priesthood is a vast improvement over the Law of Moses, for it gives us this direct relationship.

And it was not without an oath! Others became priests without any oath, but he became a priest with an oath when God said to him:

“The Lord has sworn
    and will not change his mind:
    ‘You are a priest forever.’”

Because of this oath, Jesus has become the guarantor of a better covenant.

Hebrews 7:20-22

Melchizedek became a high priest, not because he inherited it, but because God directly intervened in the process to appoint him… and He swore an oath that it should be so: Powerful stuff. Because of it Jesus is the guarantor of a better covenant, and that pretty much says it all.

 Now there have been many of those priests, since death prevented them from continuing in office; but because Jesus lives forever, he has a permanent priesthood. Therefore he is able to save completely those who come to God through him, because he always lives to intercede for them.

Such a high priest truly meets our need—one who is holy, blameless, pure, set apart from sinners, exalted above the heavens. Unlike the other high priests, he does not need to offer sacrifices day after day, first for his own sins, and then for the sins of the people. He sacrificed for their sins once for all when he offered himself. For the law appoints as high priests men in all their weakness; but the oath, which came after the law, appointed the Son, who has been made perfect forever.

Hebrews 7:23-28

I think these final verses are pretty obvious and no further words are necessary from me.  We have arrived at the point where the superiority of Jesus as our high priest is obvious to all, and the author is moving on to a discussion of the New Covenant.