Secret intimate time (6)
I believe the answer is:
closet
'secret' is the definition.
('closet' can be a synonym of 'secret')
'intimate time' is the wordplay.
'intimate' becomes 'close' ('close' can be similar in meaning to 'intimate').
'time' becomes 't'.
'close'+'t'='CLOSET'
(Other definitions for closet that I've seen before include "Small room or wardrobe" , "American cupboard or wardrobe" , "Private room; cupboard" , "A small room or cupboard" , "Covert" .)