Hebrews 7:12-25 English Standard Version (ESV)
12 For when there is a change in the priesthood, there is necessarily a change in the law as well. 13 For the one of whom these things are spoken belonged to another tribe, from which no one has ever served at the altar. 14 For it is evident that our Lord was descended from Judah, and in connection with that tribe Moses said nothing about priests.
15 This becomes even more evident when another priest arises in the likeness of Melchizedek, 16 who has become a priest, not on the basis of a legal requirement concerning bodily descent, but by the power of an indestructible life. 17 For it is witnessed of him,
“You are a priest forever,
after the order of Melchizedek.”
18 For on the one hand, a former commandment is set aside because of its weakness and uselessness 19 (for the law made nothing perfect); but on the other hand, a better hope is introduced, through which we draw near to God.
20 And it was not without an oath. For those who formerly became priests were made such without an oath, 21 but this one was made a priest with an oath by the one who said to him:
“The Lord has sworn
and will not change his mind,
‘You are a priest forever.’”
22 This makes Jesus the guarantor of a better covenant. (C.O. bible gateway.)
Let's take a look at Heb 7 starting at verse 11.
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?
For through the tribe of Levi was the priesthood according to the Law. of which Aaron was of.
12 For (BECAUSE) when there is a change in the priesthood, there is
necessarily a change in the law as well.
Because there is a change in the priesthood there is necessarily a change in the Law also because the Law states the priesthood be through Aaron not Melchizedek.
This is confirmed in the following verses in which you shared.
13 For (BECAUSE) the one of whom these things are spoken belonged to another tribe, from which no one has ever served at the altar.
14 For (BECAUSE) it is evident that our Lord was descended from Judah, and in connection with that tribe Moses said nothing about priests.
According to context the change in the Law was that which mandated who was to be priests. That is all that is stated here in Hebrews 7.
Let's jump to Hebrews chapter 8 now.
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:
So if the GOD's laws are in our hearts and minds the ministration has changed also. The ministration went from the priests sharing the the book of the Law from parchment and that which was written of GOD on Tables of stone to the LORD writing HIS Laws in our hearts and minds.
Forasmuch as ye are manifestly declared to be the epistle of Christ ministered by us, written not with ink, but with the Spirit of the living God; not in tables of stone, but in fleshy tables of the heart. And such trust have we through Christ to God-ward: Not that we are sufficient of ourselves to think any thing as of ourselves; but our sufficiency is of God;
(2Co 3:3-5 KJV)
The New Covenant GOD's Laws in our hearts and minds.
Heb 8:13 In that he saith, A new covenant, he hath made the first old. Now that which decayeth and waxeth old is ready to vanish away.
SO Say not in thine heart, Who shall ascend into heaven? (that is, to bring Christ (word; GOD's Law) down from above) Or, Who shall descend into the deep? (that is, to bring up Christ (word; GOD's Law) again from the dead.) But what saith it? The word is nigh thee, even in thy mouth, and in thy heart: that is, the word (Christ) of faith, which we preach; For Christ (the Word in the heart and mouth) is the end of the law (on parchment and Tables of Stone) for righteousness to every one that believeth.
(Rom 10:4-8; Deut 30:11 -14)