Small outbuilding is close (4)
I believe the answer is:
shut
'is close' is the definition.
(I've seen this before)
'small outbuilding' is the wordplay.
'small' becomes 's' (abbreviation - e.g. clothes size).
'outbuilding' becomes 'hut' (I am not sure about this - if you are sure you should believe this answer much more).
's'+'hut'='SHUT'
Can you help me to learn more?
(Other definitions for shut that I've seen before include "Push to" , "Draw to" , "See 19" , "Closed" , "Close" .)