Wager placed by a second Greek character (4)
I believe the answer is:
beta
'greek character' is the definition.
(letter from the Greek alphabet)
'wager placed by a' is the wordplay.
'wager' becomes 'bet' (synonyms).
'placed by' means one lot of letters go next to another.
'bet'+'a'='BETA'
'second' is the link.
I am not very happy about this link. It may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for beta that I've seen before include "2nd letter of Greek alphabet" , "It's next after alpha" , "Greek character - not quite top-notch" , "second class grade?" , "Letter before gamma" .)