late 13c., nonnerie, "nunhood, the life of nuns," from nun + -ery or from Old French nonnerie. Meaning "convent or cloister for the exclusive use of nuns" is from c. 1300. Transferred meaning "house of ill fame" is attested by 1590s.
Old English nunne "woman devoted to religious life under vows of celibacy, poverty, and obedience to a superior," also "vestal, pagan priestess," from Late Latin nonna "nun, tutor," originally (along with masc. nonnus) a term of address to elderly persons, perhaps from children's speech, reminiscent of nana (compare Sanskrit nona, Persian nana "mother," Greek nanna "aunt," Serbo-Croatian nena "mother," Italian nonna, Welsh nain "grandmother;" see nanny).
word-forming element making nouns meaning "place for, art of, condition of, quantity of," from Middle English -erie, from Latin -arius (see -ary). Also sometimes in modern colloquial use "the collectivity of" or "an example of."
<a href="https://www.etymonline.com/word/nunnery">Etymology of nunnery by etymonline</a>
Harper, D. (n.d.). Etymology of nunnery. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/nunnery