Jesus, a king and high priest after the order of Melchizedek

Melchizedek was one of several OT types and shadows of the future Messiah. However, Melchizedek had shared to some degree in the nature and offices of the Lord. One such semblance was the order from which Melchizedek received his postiion of authority. He was not a priest after the order of the Levites. This was instructive to the OT Jews regarding the importance of that king as Abraham gave a tenth of his spoils to him. Abraham was clearly inferior to Melchizedek Hebrews 7:7-8. It can even be argued that Levi, himself, gave tithes to Melchizedek. Hebrews 7:9-10
So, Jesus is not after the order of Levi, being of Judah, but of the order typified by Melchizedek being greater than Levi.

The significance of this was great since the offices of priest and king were always separate as priests could originate only from the tribe of Levi, and kings from Judah. However, in the passage you sited from Zecharia, God had provided another symbol which pointed to the future Messiah: a ceremony, followed by an icon to be displayed in the temple.

11Take from them silver and gold, and make a crown, and set it on the head of Joshua, the son of Jehozadak, the high priest. 12And say to him, ‘Thus says the Lord of hosts, “Behold, the man whose name is the Branch: for he shall branch out from his place, and he shall build the temple of the Lord. 13It is he who shall build the temple of the Lord and shall bear royal honor, and shall sit and rule on his throne. And thereb shall be a priest on his throne, and the counsel of peace shall be between them both.”’ 14And the crown shall be in the temple of the Lord as a reminder"

claninja said:

Genesis 14:18
What does it mean that Jesus became a high priest after the order of Melchizedek?

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Melchizedek was king and priest of Salem (Hebrew letters spell Shalom, or Peace). This person could only have been one man: Shem. Shem, the firstborn son of Noah was the oldest man at the time, and was himself in the unique position of being both a king over his brothers, his descendants, and priest of the world until his death during the time of Isaac. Shem was the firstborn son of Noah, which placed upon him the responsibility of serving as priest for his family, and thus was the priest of the whole world (which was his entire family) at the time. This also gave him a kingship over his brothers, and later kingship over own descendants (until they rebelled via their idolatry, most likely only leaving Salem as the last place of his kingly dominion) all the way down to the time of Isaac. When Shem died, the kingly and priestly order was legally passed on to the surviving elder firstborns (by birthright) of all the families of the world, which for Abraham's family meant that Isaac would take it, then Jacob, then Reuben, then all the firstborns of the 12 tribes. Only when G-d instituted the Aaronic priesthood did G-d require the redemption of all firstborn males in Israel so that the Aaronic priesthood would have legal legitimacy to continue as a priesthood for all Israel, not just individual families. The kingship over Israel however, was passed down by decree by the ruler of the family, Jacob, to Judah when he gave his prophecy that the "cepter shall not part" from Judah.

The order of Melchizedek is therefore a royal holy priestly order of the firstborn that existed since creation. Jesus, who comes in that order, is therefore king of the world, and priest of the world... by right of being the "firstborn of all creation." He does not need to come and serve as an Aaronic priest, but he does need to be a descendant of Judah in order to also be king of not just the world, but over all Israel.