Committee adviser bridles at pundit (11)
I believe the answer is:
commentator
'pundit' is the definition.
(I've seen this before)
'committee adviser bridles at' is the wordplay.
'committee' becomes 'com' (abbreviation for committee).
'adviser' becomes 'mentor' (I've seen this before).
'bridles' means one lot of letters goes inside another (bring something in under control).
'mentor' enclosing 'at' is 'mentator'.
'com'+'mentator'='COMMENTATOR'
(Other definitions for commentator that I've seen before include "Critic" , "Broadcaster describing sports events" , "One who reports on sports event" , "pundit" , "Sports match reporter" .)