All right, a Greek character follows the animal (5)
I believe the answer is:
okapi
'the animal' is the definition.
(I've seen this before)
'all right a greek character follows' is the wordplay.
'all right' becomes 'ok' ('ok' can be a synonym of 'all right').
'greek character' becomes 'pi' (letter from the Greek alphabet).
'follows' says to put letters next to each other.
'ok'+'a'+'pi'='OKAPI'
(Other definitions for okapi that I've seen before include "Shy Zairean ruminant" , "Giraffe-like mammal" , "Central African animal" , "Wild animal" , "Ruminant mammal of Africa" .)