So back to Hebrews 7 for what it is actually saying,
It is clearly talking about he law of priesthood which says:
Num 8:19 And I have given the Levites as a gift to Aaron and to his sons from among the children of Israel, to do the service of the children of Israel in the tabernacle of the congregation, and to make an atonement for the children of Israel: that there be no plague among the children of Israel, when the children of Israel come nigh unto the sanctuary.
The description of their work is best seen in the book of Leviticus. Leviticus 8 is about the dedication of Aaron and his sons as priests.
One could say much more on this but the Law is clear that the Priesthood was Held by Aaron and his sons and the Levites were given to Aaron to serve in the temple work of redemption.
Hebrews makes the point that there has been a change of priesthood. Now to a Jew this is impossible if one reads the OT with a veil over their eyes. The law says God chose Aaron and his sons and the tribe of Levi to minister in the tabernacle. SO naturally the Author of Hebrews has to offer some evidence form the scripture that this is so. Some proof from the OT that the priesthood would change. And rightly so, we should never accept someones teachings unless they are backed up by the scriptures.
The author of Hebrews does exactly that, they are not made up they are in the scripture. So He begins in chapter 5 to establish his proof that this is so.
Psa 2:7 I will declare the decree: the LORD hath said unto me, Thou art my Son; this day have I begotten thee.
and
Psa 110:4 The LORD hath sworn, and will not repent, Thou art a priest for ever after the order of Melchizedek.
so Here the Author establishes that the Messiah would come and He by the will of God would be a priest forever but not of the order of Aaron but rather of Melchizedek. The OT spoke of a change of the law concerning the priesthood.
SO then all the author does in between these things is show that Jesus is the Messiah and thus the new and better priest who offered himself as a sacrifice and now lives and lives forever the new priest.
But he does not stop there he goes on in chapter 8 to make a point that this priest/Jesus also has a temple he ministers in:
Heb 8:1 Now of the things which we have spoken this is the sum: We have such an high priest, who is set on the right hand of the throne of the Majesty in the heavens;
Heb 8:2 A minister of the sanctuary, and of the true tabernacle, which the Lord pitched, and not man.
Heb 8:3 For every high priest is ordained to offer gifts and sacrifices: wherefore it is of necessity that this man have somewhat also to offer.
Heb 8:4 For if he were on earth, he should not be a priest, seeing that there are priests that offer gifts according to the law:
Heb 8:5 Who serve unto the example and shadow of heavenly things, as Moses was admonished of God when he was about to make the tabernacle: for, See, saith he, that thou make all things according to the pattern shewed to thee in the mount.
notice again he uses the OT to make his point:
Exo 25:8 And let them make me a sanctuary; that I may dwell among them.
Exo 25:9 According to all that I shew thee, after the pattern of the tabernacle, and the pattern of all the instruments thereof, even so shall ye make it.
God gave Moses a pattern to copy, it says in Hebrews that it was a shadow of the heavenly temple.
Here he spells it out again:
Heb 9:11 But Christ being come an high priest of good things to come, by a greater and more perfect tabernacle, not made with hands, that is to say, not of this building;
So then what happens to the law in general?
Notice the Author again uses the OT to show what happens to the law:
Heb 8:10 For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people:
Heb 8:11 And they shall not teach every man his neighbour, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest.
Heb 8:12 For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more.
This is quoted form here:
Jer 31:31 Behold, the days come, saith the LORD, that I will make a new covenant with the house of Israel, and with the house of Judah:
Jer 31:32 Not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt; which my covenant they brake, although I was an husband unto them, saith the LORD:
Jer 31:33 But this shall be the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people.
Jer 31:34 And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.
Now we know what happens to the law it is placed in the heart and minds of the people. Note there is no indication anywhere wither here nor in the OT that Gods law has changed other than it is now in the heart and mind of the people. The covenant has changed but not the law. You may say are they not one and the same? Well no, a covenant is a promise this promise is just better thus the old promise is dissapering in light of the new promise. The old promise dissapeared because as the author said in Hebrews 8 they did not continue in Gods promise/covenant. Thus God abandoned them to their choice but made a new promise through Jeremiah that He would take his laws and write them in their hearts. The same God who wrote on stone would now write on the heart.
Keep in mind the role of a priest is to minister for those who sin/break Gods law. There is still the ark of the covenant in the heavenly which was the true the earthly temple was a copy.
John actually saw it when he had his vision of the last days:
Rev 15:5 And after that I looked, and, behold, the temple of the tabernacle of the testimony in heaven was opened:
The testimony is the 10 commandments.
Exo 25:21 And thou shalt put the mercy seat above upon the ark; and in the ark thou shalt put the testimony that I shall give thee.
Exo 25:22 And there I will meet with thee, and I will commune with thee from above the mercy seat, from between the two cherubims which are upon the ark of the testimony, of all things which I will give thee in commandment unto the children of Israel.
So John sees the ark in the temple in heaven right at the end with the testimony/10 commandments. And indeed anyone that has studied the OT knows that the reason a priest is needed is to minister for those who have broken the law and then repented thus the minister/priest ministers forgiveness for them. Sorry for length tried to keep it short, so did not quote everything one could quote.
But note the OT agrees with the NT and The NT derives its proof from the OT. This is for those who are interested.