Persuaded swimmer to cover cut (6)
I believe the answer is:
coaxed
'persuaded' is the definition.
(coaxing is a kind of persuading)
'swimmer to cover cut' is the wordplay.
'swimmer' becomes 'cod' (type of fish).
'to cover' is an insertion indicator.
'cut' becomes 'axe' (both can mean to cancel or remove).
'cod' going around 'axe' is 'COAXED'.
(Other definitions for coaxed that I've seen before include "Persuaded by fondling or flattery" , "Cajoled, inveigled" , "Persuaded gently" , "Cajoled, persuaded with soft talk" , "Wheedled, cajoled" .)