The most common and most likely answer to this crossword clue is the 6 letter word STIGMA
I've seen this crossword clue in The Times
S
T
I
G
M
A
More clues leading to the result STIGMA
- A mark, good? It’s the reverse — a bad one
- “T” in “S” as a brand
- Letter to Greeks — about time — becomes disgrace
- Spot Greek character crossing junction
- Bad mark? It’s replaced by good mark: 50 per cent
- Unwelcome mark: it's overturned by good student
- Every so often, setting a mean mark!
- Greek character concealing source of this disgrace
- Mark a git’s been given, being contrary – disgrace
- Brand magistrate crooked after waiving of charge
Buddy explains!

The straight part
We know that "disgrace" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case disgrace = stigma.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does STIGMA mean?
STIGMA noun- A mark of infamy or disgrace.
- A scar or birthmark.
- (chiefly in the plural stigmata) A mark on the body corresponding to one of the wounds of the Crucifixion on Jesus' body, and sometimes reported to bleed periodically.
- The sticky part of a flower that receives pollen during pollination.
- A visible sign or characteristic of a disease.
- A ligature of the Greek letters sigma and tau, (Ϛ/ϛ).