To tire is an old (very old) word that meant to dress, or to put clothes on. That might be a starting point. The tiring room in a theatre was the room where the actors put their costumes on.
I think there must be a misprint in the clue. The solution to 23 Down in this crossword is TIER. If the clue was "Habit 23 changes after a time" (instead of "10 changes") then ATTIRE is the perfect answer.