expert, teacher, master, model, exemplar, army (incl. counter), war
師 centers on a person who leads or serves as a standard: an expert, teacher, or master who models correct behavior, and by extension a military leader or army unit.
師 originally combined 帀 (to go around) with an element representing a mound or group, suggesting a leader who surrounds or commands a group. The modern form retains the right-side 帀 component.
The right side 帀 looks like a banner or flag, and the left side suggests a person. Picture a teacher or general standing beside a banner, leading and setting an example.
For シ, imagine a master teacher pointing at a sheet of paper: sheet -> シ, and the teacher is showing the correct model.
teacher; instructor
doctor; physician
speaker; lecturer
master; teacher
pastor; minister; clergyman; reverend
fisherman
pharmacist; chemist
diviner; fortune teller; soothsayer
engineer; technician
(army) division
instructor (esp. of martial or traditional arts); teacher; master; coach
Buddhist priest; bonze
missionary
teacher (to whom one owes a debt of gratitude); mentor; one's former teacher
studying under; looking up to; apprenticing oneself to
hunter; huntsman
teacher and student
great teacher (i.e. a buddha, bodhisattva or high monk, esp. Kobo Daishi)
twelfth month (esp. of the lunar calendar); December
medical association
(home) tutor; private tutor; private teacher
dentist
(hospital) nurse; registered nurse; RN
beautician; cosmetician; hairdresser; hair stylist