Small building is closed first off (3)
I believe the answer is:
hut
'small building' is the definition.
'closed first off' is the wordplay.
'closed' becomes 'shut' ('shut' can be a synonym of 'closed').
'first off' means to remove the first letter.
'shut' with its first letter taken away is 'HUT'.
'is' is the link.
(Other definitions for hut that I've seen before include "Shanty" , "Small wooden shelter" , "Small structure as for watchman" , "Small shed for storing, say, garden tools" , "Simple house or shelter" .)