Greek character taking time to make mark (6)
I believe the answer is:
Here is my best explanation:
'mark' is the definition.
('stigma' can be a synonym of 'mark')
'greek character taking time' is the wordplay.
'greek character' becomes 'sigma' (letter from the Greek alphabet**).
'taking' indicates putting letters inside.
'time' becomes 't'.
'sigma' going around 't' is 'STIGMA'.
'to make' is the link.
(Other definitions for stigma that I've seen before include "A mark of shame", "Mark of infamy or disgrace", "Sign of disgrace", "A stain as on character", "Brand or mark of infamy", "badge", "Blot", "Symbol of disgrace or infamy", "Part of a flower" and "Disgrace".)