Revolutionary radical's cigar (7)
I believe the answer is:
cheroot
'cigar' is the definition.
(cheroot is a kind of cigar)
'revolutionary radical's' is the wordplay.
'revolutionary' becomes 'che' (Che Guevara the Marxist revolutionary**).
'radical' becomes 'root' ('root' can be a synonym of 'radical').
'che'+'root'='CHEROOT'
(Other definitions for cheroot that I've seen before include "With both ends cut off squarely, is smoked" , "Cigar cut at both ends" , "One smoked" , "Havana?" , "Cigar with open ends - hot core (anag)" .)