Alma referred to priests who were ordained “after the order of his Son” (Alma 13:1). The phrase after the order of his Son is a reference to the Melchizedek Priesthood. In modern revelation, the Lord stated that before the days of Melchizedek, the priesthood was called “the Holy Priesthood, after the Order of the Son of God. But out of respect or reverence to the name” of God, the name was changed to the Melchizedek Priesthood (D&C 107:3–4).
Elder Bruce R. McConkie (1915–85) of the Quorum of the Twelve Apostles explained why Alma 13, like many other passages in the Book of Mormon, does not distinguish between priests of the Aaronic Priesthood and high priests of the Melchizedek Priesthood: “Book of Mormon prophets gave the title priest to officers known in this dispensation as high priests. That is, they were priests of the Melchizedek Priesthood, or as Alma expressed it, ‘the Lord God ordained priests, after his holy order, which was after the order of his Son.’ (Alma 13:1–20.)” (Mormon Doctrine, 2nd ed. [1966], 599).