'That's disgusting,' said this Greek character (3)
I believe the answer is:
phi
'this greek character' is the definition.
(letter from the Greek alphabet)
'that's disgusting said' is the wordplay.
'that's disgusting' becomes 'fi' (fi can be an expression of disgust).
'said' indicates a 'sounds like' (homophone) clue.
'fi' sounds like 'PHI'.
(Other definitions for phi that I've seen before include "Greek letter; sounds like expression of disgust" , "One Greek" , "classic character" , "Greek letter; hip (anag.)" , "Greek letter, spoken as f" .)