Elizabeth's little flutter (3)
I believe the answer is:
bet
'flutter' is the definition.
(flutter can mean a small bet)
'elizabeth's little' is the wordplay.
'elizabeth' becomes 'beth'.
'little' means to remove the last letter (the word is not quite complete).
'beth' with its final letter taken away is 'BET'.
(Other definitions for bet that I've seen before include "Wager, speculate" , "Wager, gamble" , "Money risked on a gamble" , "Wager, or the sum waged" , "'Stake, wager (3)'" .)