Take a punt on a Greek character (4)
I believe the answer is:
beta
'a greek character' is the definition.
(letter from the Greek alphabet)
'take a punt' is the wordplay.
'take' becomes 'be' (being is a kind of taking).
'a punt' becomes 'ta' (I am not sure about this - if you are sure you should believe this answer much more).
'be'+'ta'='BETA'
'on' acts as a link.
Can you help me to learn more?
(Other definitions for beta that I've seen before include "Second-class" , "second class grade?" , "Second Greek letter, B" , "Second-rate" , "Greek letter -- second in order of importance" .)