Synonyms for Supervise:

n.

look after, watch over. supervise (noun)
manage, monitor, superintend, oversee, ride herd on.

v.

control (verb)
command, steer, control, lead, manage, superintend, administer, preside, harness, order, bridle, direct, discipline, govern, dominate, execute, rule, oversee, pilot.
direct (verb)
master, lord, boss, conduct.
manage people, project (verb)
conduct, administer, look after, boss, superintend, oversee, ride herd on, control, direct.

Other synonyms:

watch over. look after. chaperon
watch over.
Other relevant words:
watch over, ride herd on, look after, monitor.