Just beat Greek character quietly (3)
I believe the answer is:
pip
'just beat' is the definition.
(as in pipping someone to the post)
'greek character quietly' is the wordplay.
'greek character' becomes 'pi' (letter from the Greek alphabet).
'quietly' becomes 'p' (p for piano and quiet).
'pi'+'p'='PIP'
(Other definitions for pip that I've seen before include "Greenwich time signal" , "Annoyed" , "Just defeat; apple seed" , "Philip" , "Dickens hero" .)