A crime to send back racehorse (6)
I believe the answer is:
murder
'a crime' is the definition.
(I know that murder is a type of crime)
'send back racehorse' is the wordplay.
'send back' shows that the letters should be reversed in order.
'racehorse' becomes 'Red Rum' (three time winner of the Grand National).
'redrum' in reverse letter order is 'MURDER'.
'to' is the link.
(Other definitions for murder that I've seen before include "Situation causing hardship" , "very difficult task" , "Dispatch" , "Slay; bump off" , "Killing most foul" .)