I thought he was a priest himself , being from the order a melchizedek a priest forever. Hence Jesus shared that lineage not as a levite but from Juda(Judea?).
Melchizedek lived hundreds of years before Judah was even born. There is no record that Melchizedek had descendants; we don’t know.
Melchizedek was not a priest thru physical lineage, and, like Melchizedek, neither would Jesus be a priest thru physical lineage.
Of 12 tribes, the tribe of Levi was set apart for religious duties. Within that tribe, it was Aaron and his sons who were appointed to be the first priests, Aaron being the high priest (
Ex. 28 and
Num. 16:8 et seq.) Only descendants of Aaron could be priests. It’s called the Aaronic priesthood. The other members of the tribe of Levi had various other duties.
There may be differing opinions as to whether or not David was considered a priest - presumably because of how great a king he was. Mention is made of how he
and his men ate the Bread of the Presence (
1 Samuel 21) which only priests could eat. However, to my knowledge no one has ever claimed that his men must also have been priests since they ate the Bread of the Presence too.
Jesus indicates allowance was made because of need in the above instance:
Mt. 12: 1-4 … He said to them, “Have you not read what David did, when he was hungry, and those who were with him: 4 how he entered the house of God and ate the bread of the Presence, which it was not lawful for him to eat nor for those who were with him, but only for the priests?
Psalm 110 is sometimes said to refer to David as being a priest like Melchizedek. But the psalm says “you are a priest for ever after the order of Melchizedek”. I don’t think David is considered to have an eternal priesthood. The psalm verse is most often seen as messianic - fulfilled in Jesus, our eternal priest. Paul speak of it in his letter to the Hebrews
5:1-10. See also Hebrews 6:20 thru 7:28.