Greek character involved in slight makes Cretan cross (8)
I believe the answer is:
minotaur
'cretan cross' is the definition.
(mythical hybrid of Crete)
'greek character involved in slight' is the wordplay.
'greek character' becomes 'tau' (letter from the Greek alphabet).
'involved in' indicates putting letters inside.
'slight' becomes 'minor' (I've seen this in another clue).
'tau' put inside 'minor' is 'MINOTAUR'.
'makes' acts as a link.
(Other definitions for minotaur that I've seen before include "Mythical bull-headed monster" , "Mythological man-bull" , "Beast of legend" , "Cretan labyrinth resident" , "Mythical man-bull" .)