Clergyman's soft with that lady in Slough (8)
I believe the answer is:
shepherd
'clergyman's' is the definition.
(shepherd is a kind of clergyman)
'soft with that lady in slough' is the wordplay.
'soft' becomes 'p' (musical abbreviation for 'piano').
'with' means one lot of letters go next to another.
'that lady' becomes 'her' (I've seen this before).
'in' indicates putting letters inside.
'slough' becomes 'shed' (both can mean to remove or lose).
'p'+'her'='pher'
'pher' inserted within 'shed' is 'SHEPHERD'.
(Other definitions for shepherd that I've seen before include "Herdsman" , "has a pie of his own" , "Farm worker" , "Steer" , "One tending a flock" .)