Justify opening of vaudeville show (9)
I believe the answer is:
vindicate
'justify' is the definition.
('vindicate' can be a synonym of 'justify')
'opening of vaudeville show' is the wordplay.
'opening of' suggests taking the first letters.
'show' becomes 'indicate' ('indicate' can be a synonym of 'show').
The initial letter of 'vaudeville' is 'v'.
'v'+'indicate'='VINDICATE'
(Other definitions for vindicate that I've seen before include "Show to be right or justified" , "Justify by evidence or results" , "Justify or exonerate" , "Avenge or exonerate" , "Divine cat (anag.)" .)