Impolite, but not quite coarse (4)
I believe the answer is:
rude
'impolite' is the definition.
(similar in meaning)
'not quite coarse' is the wordplay.
'not quite' means to remove the first letter.
'coarse' becomes 'crude' (synonyms).
'crude' with its first letter taken away is 'RUDE'.
'but' acts as a link.
(Other definitions for rude that I've seen before include "Base" , "Uncultivated" , "Coarse, unpolished" , "Impolite or coarse" , "Ill-mannered and coarse" .)