Caught reviewing some exercise by department head (7)
I believe the answer is:
trapped
'caught' is the definition.
(trapping is a kind of catching)
'reviewing some exercise by department head' is the wordplay.
'reviewing' shows that the letters should be reversed in order (I've seen 'reviews' mean this (view the letters another way)).
'some' becomes 'part' (only part of something).
'exercise' becomes 'pe' (Physical Education).
'by department head' becomes 'd' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'part' reversed gives 'trap'.
'trap'+'pe'+'d'='TRAPPED'
Can you help me to learn more?
(Other definitions for trapped that I've seen before include "Stuck" , "Ensnared, cornered" , "Caught" , "Snared" , "in a tight corner" .)