Bad behaviour, not very cool (3)
I believe the answer is:
ice
'cool' is the definition.
(icing is a kind of cooling)
'bad behaviour not very' is the wordplay.
'bad behaviour' becomes 'vice'.
'not' indicates named letters should be taken away.
'very' becomes 'v' (abbreviation).
'vice' with 'v' removed is 'ICE'.
(Other definitions for ice that I've seen before include "Formality" , "If it's thin, skating on it can be dangerous" , "Some number" , "Do cake decoration" , "Decorate with frosting" .)