Translation
For a change of law takes place out of necessity upon the changing of the priesthood.
Go to footnote numberParaphrase
For changes to the laws themselves must inevitably take place whenever there is a change in the office of the priesthood.
Footnotes
1
This word can mean either “the priesthood” or “the office of the priesthood.” The intent is similar, but speaking of it as an office makes it clear that it is much more than a single person and lives on after one man is dead.
New Priesthood, New Laws
Because the priesthood and the laws they administered on behalf of the people were intrinsically held together, changes to the office of the priesthood would require changes to the laws as well. To make the claim that Jesus was the new High Priest was a big claim because it would require major changes to the system/office of the priesthood itself and also to the laws connected to it. This passage proves that Jesus replaced the entire priesthood with Himself. I also believe its mention of changes to the laws means that obedience to the specific regulations of the Former Covenant was no longer needed, only obedience to the principles behind the regulations. This last part is not stated here, but it can be gleaned from studying the Law, the prophets, the words of Jesus, of Paul and other part of Hebrews.