Start of tragedy framed by Greek character's disgrace (6)
I believe the answer is:
stigma
'disgrace' is the definition.
(thesaurus)
'start of tragedy framed by greek character's' is the wordplay.
'start of' says to take the initial letters.
'framed by' means one lot of letters goes inside another.
'greek character' becomes 'sigma' (letter from the Greek alphabet**).
The first letter of 'tragedy' is 't'.
't' put into 'sigma' is 'STIGMA'.
(Other definitions for stigma that I've seen before include "A stain as on character" , "Part of a flower" , "Disgraceful sign" , "Badge of shame" , "Sign of disgrace" .)