'Levitical' in the Bible

But this person [Melchizedek] who is not from their Levitical ancestry received tithes from Abraham and blessed him who possessed the promises [of God].

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?