What priesthood was Elijah to reveal

John A. Widtsoe (Quorum of the Twelve)

The beginning and the end of the gospel is written in section two of the Doctrine and Covenants. It is the keystone of the wonderful gospel arch; and if that center stone should weaken and fall out, the whole gospel structure would topple down in unorganized doctrinal blocks. (CR, Apr. 1960, p. 48)

Vs. 1—"… I will reveal unto you the Priesthood, by the hand of Elijah the prophet…"

Ezra Taft Benson (Quorum of the Twelve)

What priesthood was Elijah to reveal? John the Baptist restored the keys to the Aaronic Priesthood. Peter, James, and John restored the keys of the kingdom of God. Why send Elijah?

“Because he holds the keys of the authority to administer in all the ordinances of the priesthood,” or the sealing power. (Teachings, p. 172; italics added.) So said the Prophet Joseph Smith!

The Prophet Joseph said further that these keys were “the revelations, ordinances, oracles, powers and endowments of the fulness of the Melchizedek Priesthood and of the kingdom of God on the earth.” (Teachings, p. 337; italics added.)

Even though the Aaronic Priesthood and Melchizedek Priesthood had been restored to the earth, the Lord urged the Saints to build a temple to receive the keys by which this order of priesthood could be administered on the earth again, “for there [was] not a place found on earth that he may come to and restore again that which was lost … even the fulness of the priesthood.” (D&C 124:28; italics added.) (Ensign, Aug. 1985, 6)

http://scottwoodward.org/dc2-commentary-prophetic.html