Motive behind miscreant'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 miscreant'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 last letter of 'miscreant' is 't'.
'reason' after 't' is 'TREASON'.
(Other definitions for treason that I've seen before include "Lese-majesty" , "subversion" , "Offence against state" , "Stare on (anag.)" , "Betrayal of one's nation" .)