What does the cryptic crossword clue "Arsenal supporter heading off into New York women's house (7)" mean?

The wordplay uses a container (one word inside another). UNNER (synonym="Arsenal supporter") in NY (synonym="NY") = NUNNERY The answer is NUNNERY.

Arsenal supporter heading off into New York women's house (7)

Guardian Cryptic #29256 | 17 Down | 2023-12-18 flower