Of, relating to, or characteristic of a cloister or cloistered life; quiet and orderly in a way reminiscent of monastic living.
Cloister plus the adjectival suffix -ly, which in older English (especially before the 1500s) created adjectives meaning 'of or relating to.' This is different from modern -ly which creates adverbs; 'cloisterly' preserves the older adjectival use.
English speakers stopped using -ly to create adjectives centuries ago, switching to -al, -ic, and -like instead—that's why 'cloisterly' sounds quaint, like encountering a word from a library's dustiest corner.
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