One makes a killing backing winning horse on entering (8)
I believe the answer is:
murderer
'one makes a killing' is the definition.
(murderers kill)
'backing winning horse on entering' is the wordplay.
'backing' shows that the letters should be reversed in order.
'winning horse' becomes 'Red Rum' (three-time Grand National winner).
'on' means one lot of letters go next to another.
'entering' becomes 're' (I've seen this in other clues).
'redrum' put after 're' is 'reredrum'.
'reredrum' reversed gives 'MURDERER'.
(Other definitions for murderer that I've seen before include "Serious criminal enters demurrer" , "hit man" , "Assassin" , "Criminal killer" , "One commits homicide" .)