Damage outside Eastern women's quarters (5)
I believe the answer is:
harem
'women's quarters' is the definition.
(I've seen this before)
'damage outside eastern' is the wordplay.
'damage' becomes 'harm' ('harm' can be a synonym of 'damage').
'outside' means one lot of letters goes inside another.
'eastern' becomes 'e'.
'harm' placed around 'e' is 'HAREM'.
(Other definitions for harem that I've seen before include "Women's place" , "women live here" , "Female living quarters in a Muslim household" , "Her ma (anag)" , "Collection of mates" .)