All right for a Greek character to have animal (5)
I believe the answer is:
okapi
'animal' is the definition.
(African mammal)
'all right for a greek character' is the wordplay.
'all right' becomes 'ok' (synonyms).
'for' means one lot of letters go next to another.
'greek character' becomes 'pi' (letter from the Greek alphabet).
'ok'+'a'+'pi'='OKAPI'
'to have' acts as a link.
(Other definitions for okapi that I've seen before include "African ruminant" , "Beast related to giraffe" , "creature" , "They're wild in central Africa" , "Rare mammal" .)