Bear with oddly brash character in G&S opera (4-3)
I believe the answer is:
pooh-bah
'character in gs opera' is the definition.
(character in Gilbert and Sullivan's The Mikado)
'bear with oddly brash' is the wordplay.
'bear' becomes 'pooh' (Winnie the Pooh).
'with' is a charade indicator (letters next to each other).
'oddly' means one should take alternating letters (letters in the odd-numbered positions are used).
The alternating letters of 'brash' are 'bah'.
'pooh'+'bah'='POOH-BAH'
(Other definitions for pooh-bah that I've seen before include "Pompous office-holder" , "Pompous official" , "Arrogant person of importance" .)