Get rid of a 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)
'a hut' is the second definition.
(hut in a garden)
'of' is the link.
(Other definitions for shed that I've seen before include "Outbuilding for storage" , "Abandoned" , "Lose or take off in small building" , "Separate" , "Get rid of -- moult" .)