Gelug also gives attention to monastic discipline, and is the only Vajrayana (Tibetan) school that requires monastic ordination for one to become a teacher.
In other Tantric Buddhist schools of Tibet, one could serve as a spiritual teacher while remaining a layman.
In addition to the Dalai Lamas, another priestly lineage (second in status only to the Dalai Lamas) is the Panchen Lamas.