Female meets duke in Slough (4)
I believe the answer is:
shed
'slough' is the definition.
(both can mean to remove or lose)
'female meets duke' is the wordplay.
'female' becomes 'she' (I've seen this before).
'meets' means one lot of letters go next to another.
'duke' becomes 'd' (abbreviation).
'she'+'d'='SHED'
'in' is the link.
(Other definitions for shed that I've seen before include "Outhouse -- cast" , "Basic building" , "Drop - cast off" , "In which lawnmower is kept" , "One-storeyed outbuilding" .)