She's no serious revolutionary (7)
I believe the answer is:
mildred
'she's' is the definition.
(I've seen this before)
'no serious revolutionary' is the wordplay.
'no serious' becomes 'mild' (I can't justify this - if you can you should believe this answer much more).
'revolutionary' becomes 'red' (red can informally mean communist).
'mild'+'red'='MILDRED'
Can you help me to learn more?
(Other definitions for mildred that I've seen before include "Girl" , "Woman" , "lady?" .)