Small private room near end of unit (6)
I believe the answer is:
closet
'small private room' is the definition.
(I've seen this before)
'near end of unit' is the wordplay.
'near' becomes 'close' ('close' can be a synonym of 'near').
'end of' suggests the final letters.
The last letter of 'unit' is 't'.
'close'+'t'='CLOSET'
(Other definitions for closet that I've seen before include "Small cupboard or recess" , "Study" , "Small room or wardrobe" , "Small room or cabinet for storage" , "place to store gear" .)