Sneakily managing to get rid of women's sport (7)
I believe the answer is:
angling
'sport' is the definition.
(angling is a kind of sport)
'sneakily managing to get rid of women's' is the wordplay.
'sneakily managing' becomes 'wangling' (to wangle something is to secure it dishonestly).
'to get rid of' indicates named letters should be taken away.
'women' becomes 'w'.
'wangling' with 'w' taken away is 'ANGLING'.
(Other definitions for angling that I've seen before include "Walton practised it" , "Fishing with rod and line" , "riverside activity?" , "Indirectly seeking" , "Pointing" .)