Outhouse in Slough (4)
I believe the answer is:
shed
I believe this clue is a double definition.
'outhouse' is the first definition.
(I know that shed is a type of outhouse)
'slough' is the second definition.
(both can mean to remove or lose)
'in' acts as a link.
(Other definitions for shed that I've seen before include "Get rid of - hut" , "Slough - outbuilding" , "Abandon" , "Outbuilding for storage" , "In which tools may be" .)