All the uses of the term high priesthood save one occur in the thirteenth chapter of Alma. The exceptional occurrence, in the fourth chapter is interesting because it actually defines what Alma means by the term high priesthood. In Alma 4:20, it states: “Alma delivered up the judgment seat to Nephihah, and confined himself wholly to the high priesthood of the holy order of God.” Earlier in the chapter it states that “Alma did not grant unto him [Nephihah] the office of being high priest over the church, but he retained the office of high priest unto himself; but he delivered the judgment-seat unto Nephihah” (Alma 4:18). For Alma, the term high priesthood means the office of being high priest over the church.
Thus men prepared from the foundation of the world were “called by this holy calling, and ordained unto the” office of high priest over the church (Alma 13:6). And this office of high priest over the church was "after the order of his Son, which order was from the foundation of the world." (Alma 13:7). High priests "were ordained after this manner—being called with a holy calling, and ordained with a holy ordinance, and taking upon them the" office of being high priest "of the holy order" (Alma 13:8). In sum:
In the Book of Mormon, high priest was a special office. We first hear of the office when Alma founds the church in the land of Helam (Mosiah 23:16). The office is passed to his son, Alma (Mosiah 29:42). We originally read of only one high priest, but then Alma claims that he is "a high priest over the church of God" (Alma 5:3). But perhaps he is referring to high priests chronologically as a bit later he is "the high priest over the church of God throughout the land" (Alma 8:23), and was acknowledged as such:
Now, as I said concerning the holy order, or this high priesthood, there were many who were ordained and became high priests of God; and it was on account of their exceeding faith and repentance, and their righteousness before God, they choosing to repent and work righteousness rather than to perish;
Therefore they were called after this holy order, and were sanctified, and their garments were washed white through the blood of the Lamb.
Now they, after being sanctified by the Holy Ghost, having their garments made white, being pure and spotless before God, could not look upon sin save it were with abhorrence; and there were many, exceedingly great many, who were made pure and entered into the rest of the Lord their God. (Alma 13:10–12)
we know that thou art high priest over the church which thou hast established in many parts of the land, according to your tradition; and we are not of thy church, and we do not believe in such foolish traditions. (Alma 8:11).Some time later, we hear of other high priests:
they took him, and bound him, and carried him before Ammon, who was a high priest over that people.After 3 Nephi 6:22 we hear no more of high priests. After the coming of Christ they disappear and the church seems to be led by "disciples" rather than high priests.
And it came to pass that he caused that he should be carried out of the land. And he came over into the land of Gideon, and began to preach unto them also; and here he did not have much success, for he was taken and bound and carried before the high priest, and also the chief judge over the land. (Alma 30:20–21)
Thus the high priesthood was a specific office used for at least a century among the Nephites.