Inclination of a revolutionary head to support homework (12)
I believe the answer is:
preparedness
'inclination' is the definition.
'a revolutionary head to support homework' is the wordplay.
'revolutionary head' becomes 'redness' (I can't explain this - if you can you should believe this answer much more).
'to support' means one lot of letters go next to another.
'homework' becomes 'prep' ('prep' can be a synonym of 'homework').
'a'+'redness'='aredness'
'aredness' put after 'prep' is 'PREPAREDNESS'.
'of' acts as a link.
(Another definition for preparedness that I've seen is " State of readiness".)