Private room nearby, at end of street (6)
I believe the answer is:
closet
'private room' is the definition.
(I've seen this before)
'nearby at end of street' is the wordplay.
'nearby' becomes 'close' (similar in meaning).
'at end of' suggests the final letters.
The last letter of 'street' is 't'.
'close'+'t'='CLOSET'
(Other definitions for closet that I've seen before include "Small cupboard or recess" , "US press for clothing" , "Shut away in private conference - in small room?" , "A small room - secret?" , "secret is revealed" .)