The reason he left crime (7)
I believe the answer is:
treason
'crime' is the definition.
(treason is a kind of crime)
'the reason he left' is the wordplay.
'left' is a deletion indicator (some letters have left).
'the'+'reason'='thereason'
'thereason' with 'he' taken away is 'TREASON'.
(Other definitions for treason that I've seen before include "Crime agains one's country" , "Offence against state" , "Mutiny" , "Act of betrayal of a government" , "Criminal attempt to overthrow a government" .)