Besides being a priest, what was Ezra skilled as in the Law of Moses?

Answer: A scribe

Ezra was a scribe skilled in the Law of Moses, and King Artaxerxes addressed him as Ezra the priest and scribe.

“this Ezra came up from Babylon. He was a scribe skilled in the Law of Moses, which the LORD, the God of Israel, had given. The king had granted Ezra all his requests, for the hand of the LORD his God was upon him.”— Ezra 7:6 (BSB)