Wager article is letter in Greek (4)
I believe the answer is:
beta
'in greek' is the definition.
(I know that Greek alphabet has part Beta)
'wager article' is the wordplay.
'wager' becomes 'bet' (synonyms).
'article' becomes 'a' (the indefinite article in English).
'bet'+'a'='BETA'
'is letter' is the link.
I am not very happy about this link. Some or all of 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 "Second Greek letter - beat that" , "Second-rate" , "final test" , "It's next after alpha" , "Old character" .)