'Priesthood' in the Bible

Now if there was perfection through the Levitical priesthood (for under it the people have received the law), what further need was there for another priest to arise after the order of Melchizedek, and not be called after the order of Aaron?

For the priesthood being changed, there is of necessity a change made also in the law.

For it is evident that our Lord has sprung out of Judah, about which tribe Moses spoke nothing concerning priesthood.

But he, because he lives forever, has his priesthood unchangeable.