The church of the Book of Mormon, as finalized at the time of Christ, was a structure of teacher, priest, and elder. The position of high priest was no longer required.
7 Now this was the cause of much affliction to Alma, yea, and to many of the people whom Alma had consecrated to be teachers, and priests, and elders over the church; (Alma 4:7)
1 The manner which the disciples, who were called the elders of the church, ordained priests and teachers— (Moroni 3:1)