Red paper out of very fashionable company (5)
I believe the answer is:
prada
'fashionable company' is the definition.
(Prada is a fashion house)
'red paper out of very' is the wordplay.
'red paper' becomes 'pravda' (newspaper of the Communist Party in the USSR).
'out of' is a deletion indicator.
'very' becomes 'v' (abbreviation).
'pravda' with 'v' taken out is 'PRADA'.
(Other definitions for prada that I've seen before include "Milan outfit" , "Design house" .)