Synonyms for Monastic (same or very similar meaning)
WordNet sense 1 (a male religious living in a cloister and devoting himself to contemplation and prayer and work):
monk
WordNet sense 2 (of communal life sequestered from the world under religious vows):
cloistered, cloistral, conventual, monastical
WordNet sense 3 (not concerned with the temporal world or swayed by mundane considerations):
unworldly
From the ODE community, based on WordNet
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