'Priesthood' in the Bible

Furthermore, here [in the Levitical priesthood] tithes are received by men who are subject to death; but in that case [concerning Melchizedek], they are received by one of whom it is testified that he lives on [perpetually].

Now if perfection [a perfect fellowship between God and the worshiper] had been attained through the Levitical priesthood (for under it the people were given the Law) what further need was there for another and different kind of priest to arise, one in the manner of Melchizedek, rather than one appointed to the order of Aaron?

For when there is a change in the priesthood, there is of necessity a change of the law [concerning the priesthood] as well.

but, on the other hand, Jesus holds His priesthood permanently and without change, because He lives on forever.