Motive behind convict's last crime (7)
I believe the answer is:
treason
'crime' is the definition.
(I know that treason is a type of crime)
'motive behind convict's last' is the wordplay.
'motive' becomes 'reason' (reason is a kind of motive).
'behind' is a charade indicator (letters next to each other).
'last' suggests the final letters.
The final letter of 'convict' is 't'.
'reason' put after 't' is 'TREASON'.
(Other definitions for treason that I've seen before include "attempting to overthrow the king" , "Offence against state" , "One rats (anag)" , "subversion" , "Lese-majesty" .)