Greek character has German beast (3)
I believe the answer is:
pig
'beast' is the definition.
(I know that pig is a type of animal)
'greek character has german' is the wordplay.
'greek character' becomes 'pi' (letter from the Greek alphabet).
'has' is a charade indicator (letters next to each other).
'german' becomes 'g' (abbreviation).
'pi'+'g'='PIG'
(Other definitions for pig that I've seen before include "Eat greedily" , "Eat ravenously" , "Porcine animal" , "Farm animal" , "Domestic swine" .)