Wager on a Greek character (4)
I believe the answer is:
beta
'greek character' is the definition.
(letter from the Greek alphabet)
'wager on a' is the wordplay.
'wager' becomes 'bet' (synonyms).
'on' means one lot of letters go next to another (in a down clue, letters appear on others).
'bet'+'a'='BETA'
(Other definitions for beta that I've seen before include "Second Greek letter - beat that" , "software under test" , "Second-rate" , "character in Marathon" , "Second letter of the Greek alphabet" .)