There is no Mechezidek priesthood. Only the Levitical priesthood. Yeshua is like Melchezidek because he was a King and a Priest like Melchezidek. Nope the Levites will continue to serve the Messiah in the future kingdom.
A King, who is also a Priest, has never existed in Israel’s history. The kingdom and the priesthood were always separate. The kingdom was established forever in David’s descendants, and the priesthood was established in the descendants of Levi and Aaron forever as well.
And here are some of God’s promises to the Levitical priesthood.
“And you shall gird them with sashes, Aaron and his sons, and put the hats on them. The priesthood shall be theirs for a perpetual statute, So you shall consecrate Aaron and his sons.” Exodus 29:9
“You shall put the holy garments on Aaron, and anoint him and sanctify him, that he may minister to Me as priest. And you shall bring his sons and clothe them with tunics. You shall anoint them, as you anointed their father, that they may minister to Me as priests; for their anointing shall surely be and everlasting priesthood throughouttheir generations.” Exodus 40:13-15
Then the Lord spoke to Moses, saying; “Phinehas the son of Eleazar, the son of Aaron the priest, has turned back My wrath from the children of Israel, because he was zealous with My zeal among them, so that I did not consume the children of Israel in My zeal. Therefore say, ‘Behold, I give to him My covenant of peace; and it shall be to him and his descendants after him a covenant of an everlasting priesthood, because he was zealous for his God, and made atonement for the children of Israel .’” Numbers 25;10-13
God promised the Messiah would be both king and priest like Melchizedek in Psalm 110:4. God also spoke through other prophets on numerous occasions that He would indeed bring both offices into one in the Messiah.
“Behold, the days are coming”, says the Lord, “that I will perform that good thing which I have promised to the house of Israel and to the house of Judah; In those days and at that time I will cause to grow up to David a Branchof righteousness; He shall execute judgment and righteousness in the earth. In those days Judah will be saved, andJerusalem will dwell safely. And this is the name by which she will be called; ‘THE LORD OUR RIGHTEOUSNESS’. For thus says the Lord; David shall never lack a man to sit on the throne of the house of Israel; nor shall the priests, the Levites, lack a man to offer burnt offerings before Me, to kindle grain offerings, and to sacrifice continually.” Jeremiah 33:14-18
“Behold, the man whose name is the BRANCH! From his place he shall branch out, and he shall build the temple of the Lord; Yes, he shall build the temple of the Lord. He shall bear the glory, and shall sit and rule on his throne; So he shall be a priest on his throne, and the counsel of peace shall be between them both.” (both offices) Zechariah 6:12-13
“Then it shall be the prince’s part to give burnt offerings, grain offerings, and drink offerings, at the feasts, the New Moons, the Sabbaths, and at all the appointed seasons of the house of Israel. He shall prepare the sin offering, the grain offering, the burnt offering, and the peace offerings to make atonement for the house of Israel .” Ezekiel 45:17
God had said the Levites had and “everlasting” priesthood. The only way God could fulfill these promises He made to David and the Levites is if the Messiah was from both tribes. Yeshua just so happens to be descendant of both David and Levi!