The most common and most likely answer to this crossword clue is the 9 letter word SLEAZIEST
I've seen this crossword clue in The Daily Telegraph
S
L
E
A
Z
I
E
S
T
Buddy explains!

The straight part
We know that "Most disgraceful" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case most disgraceful = sleaziest.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 SLEAZIEST mean?
SLEAZIEST adjective- Marked by low quality; inferior; inadequate.
- Raunchy or perverted in nature; tastelessly sexual
- Untrustworthy
- Thin and flimsy