Persuasive son frequently gets work over in South Ken (4-6)
I believe the answer is:
soft-spoken
'persuasive' is the definition.
(soft-spoken can mean persuasive)
'son frequently gets work over in south ken' is the wordplay.
'son' becomes 's' (genealogical abbreviation for son).
'frequently' becomes 'oft' (oft can mean frequently, eg oft-quoted).
'gets work over' becomes 'po' (I can't explain this - if you can you should give a lot more credence to this answer).
'in' means one lot of letters goes inside another.
'south' becomes 'S' (abbreviation).
's'+'ken'='sken'
'po' inserted inside 'sken' is 'spoken'.
's'+'oft'+'spoken'='SOFT-SPOKEN'
(Another definition for soft-spoken that I've seen is " Having a mild or gentle voice".)