Show flamboyant skill backing restaurant (9)
I believe the answer is:
trattoria
'restaurant' is the definition.
(I've seen this before)
'show flamboyant skill backing' is the wordplay.
'show' becomes 'air' (both can mean broadcast).
'flamboyant' becomes 'ott' (abbreviation for 'over the top').
'skill' becomes 'art' (I've seen this before).
'backing' is a reversal indicator.
'air'+'ott'+'art'='airottart'
'airottart' written backwards gives 'TRATTORIA'.
(Other definitions for trattoria that I've seen before include "Italian restaurant" , "Place to eat" , "where Italians eat" , "Italian eating establishment" .)