Insolently proud (8)
I believe the answer is:
arrogant
'insolently proud' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for arrogant that I've seen before include "Public speaker" , "Overly self-important" , "Over-cocky" , "Overbearing; conceited" , "Cocky" .)