The woman had to get rid of hut (4)
I believe the answer is:
shed
I believe this clue is a triple definition!
'the woman had' is the first definition.
(she'd)
'to get rid of' is the second definition.
(shed can mean to get rid of or discard)
'hut' is the third definition.
(hut in a garden)
(Other definitions for shed that I've seen before include "lost" , "that may be at bottom of garden?" , "Discard; small building" , "Get rid of - garden building" , "Outhouse for storing garden tools etc" .)