Curse Cornish listener (5)
I believe the answer is:
swear
'curse' is the definition.
(synonyms)
'cornish listener' is the wordplay.
'cornish' becomes 'SW' (Cornwall is in the South West of England).
'listener' becomes 'ear' (body part which hears or listens).
'sw'+'ear'='SWEAR'
(Other definitions for swear that I've seen before include "not to mince one's words" , "Utter obscenities or take an oath" , "Avow" , "Assert" , "Express annoyance" .)