The quality or state of being cloisterlike; the characteristic quietness, order, and separation from the outside world found in or associated with cloisters.
From cloisterly (adjective) plus the suffix -ness, which creates abstract nouns from adjectives. Following the pattern: cloister → cloisterly (adjective) → cloisterliness (noun expressing the quality).
This is a word you almost never encounter, which makes it a perfect example of how English speakers prefer shorter expressions: we'd just say 'peacefulness' or 'monastic calm' instead of cloisterliness, even though the longer word is perfectly logical.
Complete word intelligence in one call. Free tier — 50 lookups/day.