Problem identified by top teacher, a revolutionary (8)
I believe the answer is:
headache
'problem' is the definition.
(headache can mean a problem or annoyance)
'top teacher a revolutionary' is the wordplay.
'top teacher' becomes 'head' (headteacher).
'revolutionary' becomes 'che' (Che Guevara the Marxist revolutionary).
'head'+'a'+'che'='HEADACHE'
'identified by' acts as a link.
(Other definitions for headache that I've seen before include "Major problem" , "Worry, trouble (colloq.)" , "A pain in the brain" , "Migraine" , "Severe problem" .)