There was in the days of Herod, the king of Judea, a certain priest named Zacharias, of the division of Abijah. His wife was of the daughters of Aaron, and her name was Elizabeth. (Luke 1:5)
Zacharias was both a Levite and a priest.
Now this is the testimony of John, when the Jews sent priests and Levites from Jerusalem to ask him, “Who are you?” (John 1:19)
This says that two different types, priests and Levites were sent from Jerusalem to John.
I can understand how a Levite which describes ancestry, would not be a priest, which describes a duty or type of service. In fact that would be an accurate description for John the Baptist. He was a Levite yet he was not serving as a priest.
Was it possible for someone who was not a Levite to legitimately serve as and be called a priest?