Also known as the Melchizedek Priesthood, male, and the Magdalene Priesthood, female (Doctrines of the Saints 119:16). In Abrahamic religions, the High Priesthood is named after Melchizedek (Hebrew, “king of righteousness”), the king of Salem and High Priest of El Elyon (Hebrew, “Most High God”).
This is because the High Priesthood combines the dual position of king and Priest.
The Lord has identified the High Priesthood for women as the Magdalene Priesthood, as these women are set apart as both queens and High Priestesses. This High Priesthood, both the male and the female, are led by Jesus Christ, the One High Priest over all the earth (Psalm 110:4). All members of the High Priesthood are both representatives of and servants to Jesus Christ (Hebrews 5:6-10).
While in the time between Moses giving the Torah to Israel and the crucifixion and resurrection of Jesus Christ the Levites were the only ones with the proper authority in Israel to fill the roles of the Low or Levitical Priesthood (with the exception of times and places where there were no Levites, as seen in the Book of Mormon), the High Priesthood was available to any called of God. The High Priesthood has been on the earth at least from the time of Adam and Eve, the first High Priest and High Priestess that we are aware of.
The purpose of the High Priesthood is to bring the Heavens to the Earth, uniting the Creator and the Creation in Jesus Christ (Doctrines of the Saints 119:10). While all those that hold the High Priesthood are High Priest/High Priestesses, the offices of these brothers and sisters are divided up based on callings: Elder, High Priest, Evangelists, Patriarch/Matriarch, Seventy (Elder), Seventy (High Priest), and four degrees of Apostles.
See 1 Moses 25:24; 2 Moses 28:15; Book of the Law of the Lord 36; Genesis 14:18–20; Psalm 110:4; Zenos 9 header; Alma 10:7-15 RAV, 13:14-19 OPV; Luke 8:2; John 20:1-18; Doctrines of the Saints 5a-5b, 5g:22, 8b:32, 10b:4-6, 13b:31-32, 15d:17, 42:45, 118g:13, 119:3, 16; Michelle 1:60; Hebrews 5:6-10, 6:20, 7:1-21; Levitical Priesthood, Magdalene, Melchizedek.