In the Book of Mormon, it was the teacher who was assigned to govern the local church:
19 And it came to pass that king Mosiah granted unto Alma that he might establish churches throughout all the land of Zarahemla; and gave him power to ordain priests and teachers over every church.
20 Now this was done because there were so many people that they could not all be governed by one teacher; neither could they all hear the word of God in one assembly;
21 Therefore they did assemble themselves together in different bodies, being called churches; every church having their priests and their teachers, and every priest preaching the word according as it was delivered to him by the mouth of Alma. (Mosiah 25: 19-21)
They were able to perform baptisms as well.
13 And Alma established a church in the land of Sidom, and consecrated priests and teachers in the land, to baptize unto the Lord whosoever were desirous to be baptized. (Alma 15:13)