WordNet sense 1 (of communal life sequestered from the world under religious vows):

cloistral, monastic, conventual, monastical

WordNet sense 2 (not concerned with the temporal world or swayed by mundane considerations):

unworldly

WordNet sense 3 (providing privacy or seclusion):

reclusive, secluded, sequestered

WordNet sense 4 (confined to particular persons or groups or providing privacy):

private