Ape Greek character, Member of Parliament (5)
I believe the answer is:
chimp
'ape' is the definition.
(I've seen this before)
'greek character member of parliament' is the wordplay.
'greek character' becomes 'chi' (letter from the Greek alphabet).
'member of parliament' becomes 'mp' (I've seen this in other clues).
'chi'+'mp'='CHIMP'
(Other definitions for chimp that I've seen before include "Creature" , "Ape (colloq.)" , "Arboreal ape from equatorial Africa (abbr)" , "A great ape (abbr.)" , "Cheeky primate" .)