Small room near end of apartment (6)
I believe the answer is:
closet
'small room' is the definition.
(I've seen this before)
'near end of apartment' is the wordplay.
'near' becomes 'close' ('close' can be a synonym of 'near').
'end of' suggests the final letters.
The final letter of 'apartment' is 't'.
'close'+'t'='CLOSET'
(Other definitions for closet that I've seen before include "North American cupboard" , "A small room or cupboard" , "Secret - cupboard" , "Shut away in private conference - in small room?" , "Wardrobe in the US" .)