Wager with a foreign character (4)
I believe the answer is:
beta
'foreign character' is the definition.
(Greek letter)
'wager with a' is the wordplay.
'wager' becomes 'bet' (synonyms).
'with' means one lot of letters go next to another.
'bet'+'a'='BETA'
(Other definitions for beta that I've seen before include "Second letter of the Greek alphabet" , "In a constellation, a star second in brightness" , "second class grade?" , "sort of test" , "less than perfect mark" .)