Start of cool look with revolutionary hat (6)
I believe the answer is:
cloche
'hat' is the definition.
(I've seen this before)
'start of cool look with revolutionary' is the wordplay.
'start of' suggests taking the first letters.
'look' becomes 'lo'.
'with' is a charade indicator (letters next to each other).
'revolutionary' becomes 'che' (Che Guevara the Marxist revolutionary**).
The initial letter of 'cool' is 'c'.
'c'+'lo'+'che'='CLOCHE'
(Other definitions for cloche that I've seen before include "Transparent cover for forcing plants" , "Bell-shaped hat" , "Cover put over young plants to protect them from cold" , "Horticultural cover" , "Style of hat for a woman" .)