Yankee, say, accompanying a Greek character (4)
I believe the answer is:
beta
'greek character' is the definition.
(letter from the Greek alphabet)
'yankee say accompanying a' is the wordplay.
'yankee say' becomes 'bet' (Yankee is a type of bet).
'accompanying' means one lot of letters go next to another.
'bet'+'a'='BETA'
(Other definitions for beta that I've seen before include "final test" , "2nd letter of Greek alphabet" , "Greek letter -- second in order of importance" , "software under test" , "Greek character - not quite top-notch" .)