All right, a Greek character is an animal (5)
I believe the answer is:
okapi
'an animal' is the definition.
(African mammal)
'all right a greek character' is the wordplay.
'all right' becomes 'ok' (synonyms).
'greek character' becomes 'pi' (letter from the Greek alphabet).
'ok'+'a'+'pi'='OKAPI'
'is' acts as a link.
(Other definitions for okapi that I've seen before include "African mammal related to giraffe" , "Animal, a sort of zebra/giraffe cross" , "Horned ruminant" , "Wild African" , "Central African animal" .)