Small room shut on time (6)
I believe the answer is:
'small room' is the definition.
(I've seen this before)
'shut on time' is the wordplay.
'shut' becomes 'close' (synonyms).
'on time' becomes 't' (abbreviation. I am not sure about the 'on' bit.).
Can you help me to learn more?
(Other definitions for closet that I've seen before include "US press for clothing" , "Confine" , "little room" , "North American cupboard" , "A small room - best to come out of it" .)