Rudimentary building in Slough (4)
I believe the answer is:
shed
This clue is a double definition.
'rudimentary building' is the first definition.
(I know that shed is a type of rudimentary building)
'slough' is the second definition.
(both can mean to discard something)
'in' acts as a link.
(Other definitions for shed that I've seen before include "tools here, maybe?" , "Abandon" , "dropped" , "Jettison" , "See 12" .)