From The Mouth of David

          If perfection could have been attained through the Levitical priesthood—and indeed the law given to the people established that priesthood—why was there still need for another priest to come, one in the order of Melchizedek, not in the order of Aaron?  For when the priesthood is changed, the law must be changed also.  He of whom these things are said belonged to a different tribe, and no one from that tribe has ever served at the altar.  For it is clear that our Lord descended from Judah, and in regard to that tribe Moses said nothing about priests.  And what we have said is even more clear if another priest like Melchizedek appears, one who has become a priest not on the basis of a regulation as to his ancestry but on the basis of the power of an indestructible life.  For it is declared: “You are a priest forever, in the order of Melchizedek.” (Hebrews 7:11-17) 

          As noted before, the “You are a priest forever, in the order of Melchizedek” quote is from Psalm 110. David wrote it about a lord who was greater than he, his son who would reign forever. David knew the law. He knew that his son could never be a Levitical priest. It’s likely that he knew that Saul had attempted to act as a priest, and that the throne had been taken from him as a result. If David’s son was to reign forever, and act as priest, he had to do so under a different set of regulations. Melchizedek provided a perfect model, acting as both priest and king.

          Fifteen hundred years later, a descendant of David did come along. He could not be a Levitical priest because he was not a descendant of Levi, he was a descendant of Judah. He established that priesthood based on a new covenant in His blood, and having paid the price for our sins with that blood, and having risen from the dead to live forever more, He has been established as being of the order of Melchizedek.