Have a wager against a Greek character (4)
I believe the answer is:
beta
'greek character' is the definition.
(letter from the Greek alphabet)
'have a wager against a' is the wordplay.
'have a wager' becomes 'bet' (a wager is a bet).
'against' is a charade indicator (letters next to each other).
'bet'+'a'='BETA'
(Other definitions for beta that I've seen before include "It's next after alpha" , "Second Greek letter - beat that" , "Second-rate" , "less than perfect mark" , "second class grade?" .)