Greek character taking time to make mark (6)
I believe the answer is:
stigma
'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 "Symbol of disgrace or infamy" , "Mark of shame, stain on reputation" , "Brand or mark of infamy" , "Mark of infamy or disgrace" , "A stain as on character" .)