Haggard female has day in Slough (4)
I believe the answer is:
shed
'slough' is the definition.
(both can mean to remove or lose)
'haggard female has day' is the wordplay.
'haggard female' becomes 'she' ('she' refers to a woman. I am not sure about the 'haggard' bit.).
'has' means one lot of letters go next to another.
'day' becomes 'd' (abbreviation for day).
'she'+'d'='SHED'
'in' acts as a link.
Can you help me to learn more?
(Other definitions for shed that I've seen before include "that may be at bottom of garden?" , "Remove clothes in small hut" , "storage unit" , "Jettison" , "building away from home" .)