Aristotle contrived a system of betting! (9)
I believe the answer is:
totaliser
'a system of betting' is the definition.
(totaliser is a type of bet)
'aristotle contrived' is the wordplay.
'contrived' indicates an anagram.
'aristotle' with letters rearranged gives 'TOTALISER'.
(Other definitions for totaliser that I've seen before include "you can bet on it!" , "System of speculation" , "Betting system" , "Risky system" , "Summer" .)