Close small shack (4)
I believe the answer is:
shut
'close' is the definition.
(I know that close can be written as shut)
'small shack' is the wordplay.
'small' becomes 's' (abbreviation - e.g. clothes size).
'shack' becomes 'hut' (synonyms).
's'+'hut'='SHUT'
(Other definitions for shut that I've seen before include "Push to" , "Out of business" , "Slam" , "not accepting visitors" , "Draw to" .)