Hebrews 7

Abraham had the promise of God that had been directly spoken to him, and yet he still gave a tenth to Melchizedec. Why? Because Abraham recognized that earthly wealth was not the path to salvation and that the wealth he attained was the direct result of God. Through the priest and his tithe, he could demonstrate that knowledge. Interestingly, Melchizedec is not recorded to have had a birth or death and so he often is described as at least an archetype of the coming Messiah, distinctly different from the Levitical priests.

Part of the reason for setting up the Law and the Levitical priesthood, by extension, was to demonstrate that we cannot save ourselves and that an earthly priest cannot provide forgiveness for our sins. In spite of the fact that the Levitical priest was elevated to the highest possible level in Judaism and was responsible for providing atonement for the sins of the people, he still had to provide atonement for himself and he still died. That meant that the priest was imperfect and that the job was constantly being handed from one imperfect person to another.

Jesus wasn't from the tribe of Levi. He was from the tribe of Judah, and He turned the priesthood on its ear. He demonstrated that, like Melchizedec, there could be a priest with not beginning and no end, with no sin to atone for and with no death to fear. Once he provided atonement for the people it was done and never needed to be done again, and since He had defeated death, there would never be a need or reason to ever replace Him.