Affectedly polite chap — a slippery character (7)
I believe the answer is:
genteel
'affectedly polite' is the definition.
(I've seen this before)
'chap a slippery character' is the wordplay.
'chap' becomes 'gent' (I've seen this in other clues).
'a slippery character' becomes 'eel' (I've seen this before).
'gent'+'eel'='GENTEEL'
(Other definitions for genteel that I've seen before include "Cultured; polite" , "Marked by refinement in taste and manners" , "Courteous, well-bred" , "Well mannered" , "Courtly, cultivated" .)