Mormon Doctrine, pg. 223; “Because Elijah has come in this dispensation, the fullness of salvation is again available for the living and the dead. He “was the last prophet that held the keys of the priesthood” in ancient Israel, the Prophet said. His latter-day mission was to “restore the authority and deliver the keys of the priesthood, in order that all the ordinances may be attended to in righteousness. . . . Why send Elijah? Because he holds the keys of the authority to administer in all the ordinances of the priesthood; and without the authority is given, the ordinances could not be administered in righteousness.” (Teachings, p. 172.)”
2 Kings 2:1; “And it came to pass, when the LORD would take up Elijah into heaven by a whirlwind, that Elijah went with Elisha from Gilgal.”
Elijah did not hold any priesthood while on earth. He was a prophet who lived in the ninth century BC. Interestingly enough he placed the “mantel of prophet” on the shoulders of Elisha when the latter was out plowing a field. 1 Kings 19:19-20.