Crime? Only half of it has motive! (7)
I believe the answer is:
treason
'crime?' is the definition.
(treason is a kind of crime)
'only half of it has motive' is the wordplay.
'only half of' indicates taking half.
'has' is a charade indicator (letters next to each other).
'motive' becomes 'reason' (reason is a kind of motive).
'it' cut in half is 't'.
't'+'reason'='TREASON'
(Other definitions for treason that I've seen before include "Lese-majesty" , "Crime agains one's country" , "rebellion" , "Crime of national betrayal" , "Gunpowder Plot, say" .)