Poor grade omitted from MP’s résumé (5)
I believe the answer is:
recap
'resume' is the definition.
(recapping is a kind of resuming)
'poor grade omitted from mp's' is the wordplay.
'poor grade' becomes 'D' (an exam result).
'omitted from' indicates named letters should be taken away.
'mp' becomes 'redcap' (Military Police officers are called redcaps).
'redcap' with 'd' taken away is 'RECAP'.
(Other definitions for recap that I've seen before include "Review" , "Caper (anag)" , "Final summary" , "Go over study material again" , "sum everything up" .)