Revolutionary head shows sign of embarrassment (7)
I believe the answer is:
redness
'sign of embarrassment' is the definition.
(I've seen this in another clue)
'revolutionary head' is the wordplay.
'revolutionary' becomes 'red' (informal term for communist).
'head' becomes 'ness' (both can mean a promontory).
'red'+'ness'='REDNESS'
'shows' acts as a link.
(Other definitions for redness that I've seen before include "Inflamed appearance" , "Appearance of inflammation" .)