Get rid of the hut (4)
I believe the answer is:
shed
This clue is a double definition.
'get rid' is the first definition.
(shed can mean to get rid of or discard)
'the hut' is the second definition.
(hut in a garden)
'of' is the link.
(Other definitions for shed that I've seen before include "Small hut - lose it" , "Get rid of - outbuilding" , "Take off in hut?" , "Removed in garden hut" , "Outbuilding with a single story" .)