Angler fellow is that woman's husband (9)
I believe the answer is:
fisherman
'angler' is the definition.
(I've seen this before)
'fellow is that woman's husband' is the wordplay.
'fellow' becomes 'f' (abbreviation - of a society etc.).
'that woman's' becomes 'her' (belonging to a woman).
'husband' becomes 'man' (a married man).
'f'+'is'+'her'+'man'='FISHERMAN'
(Other definitions for fisherman that I've seen before include "He's an angler" , "He casts" , "St Peter" , "Fin masher might be all at sea" , "One possibly catching sole" .)