Blemish of Greek character -- that's about tax primarily? (6)
I believe the answer is:
stigma
'blemish' is the definition.
(stigma is a kind of blemish)
'greek character that's about tax primarily?' is the wordplay.
'greek character' becomes 'sigma' (letter from the Greek alphabet**).
'that's about' is an insertion indicator.
'primarily?' says to take the initial letters (I've seen 'primarily' mean this).
The initial letter of 'tax' is 't'.
'sigma' going around 't' is 'STIGMA'.
'of' is the link.
(Other definitions for stigma that I've seen before include "Brand or mark of infamy" , "Mark of dishonour" , "Mark of shame or social disgrace" , "part of plant" , "Symbol of disgrace or infamy" .)