Chance of donkey derby success, initially (4)
I believe the answer is:
odds
'chance' is the definition.
(I've seen this in another clue)
'of donkey derby success initially' is the wordplay.
'initially' suggests taking the first letters.
The initial letters of 'of donkey derby success' is 'ODDS'.
(Other definitions for odds that I've seen before include "prices" , "Measure of probability" , "Perhaps even money" , "Betting price" , "at which one may be disagreeing" .)