Letter to Greeks — about time — becomes disgrace (6)
I believe the answer is:
stigma
'disgrace' is the definition.
(thesaurus)
'letter to greeks about time' is the wordplay.
'letter to greeks' becomes 'sigma' (I've seen this before).
'about' means one lot of letters goes inside another.
'time' becomes 't'.
'sigma' enclosing 't' is 'STIGMA'.
'becomes' is the link.
(Other definitions for stigma that I've seen before include "part of plant" , "Disgraceful sign" , "evidence of nastiness?" , "Part of a flower" , "Disgraceful mark" .)