Luke 1:36, Elizabeth your relative. While Mary was of the royal lineage of David, she also was a relative on her mother’s side of Elizabeth, the priest-wife of Zacharias, who was a daughter of Aaron (Luke 1:5).
Does this mean that Mary was of priestly as well as Davidic lineage. No. Here is why. The Torah only required the high priest to marry within his tribal family (Lev 21:14). The Torah didn’t prohibit rank and file priests were taking a wife from another tribe. For example, Mary’s father would have been a priest, but her mother could have been from another tribe. Mary’s mother could have been a sister to Elizabeth’s mother making Mary and Elizabeth cousins. This would have made Elizabeth of priestly lineage, but not Mary. According to her genealogy, Mary was of Davidic lineage via her father.
To be sure, Yeshua was a priest, but not one of Aaronic lineage, but after the order of Melchizedek, which was the priesthood of the firstborn son passed on generationally. Yeshua was the first born son of Elohim eternally, which is why he is presently at the right hand of Elohim acting as our Great High Priest (Heb 1:3 cp. 3:1; 4:4; 8:1).