Giraffe-like animal comfortable with a Greek character (5)
I believe the answer is:
okapi
'giraffe-like animal' is the definition.
(I've seen this before)
'comfortable with a greek character' is the wordplay.
'comfortable' becomes 'OK' (OK can mean comfortable or well).
'with' says to put letters next to each other.
'greek character' becomes 'pi' (letter from the Greek alphabet).
'ok'+'a'+'pi'='OKAPI'
(Other definitions for okapi that I've seen before include "African animal related to the giraffe" , "browser" , "Animal of the giraffe family (much loved by crossword setters)" , "Wild animal" , "African ruminant" .)