The most common and most likely answer to this crossword clue is the 6 letter word SHABBY
I've seen this crossword clue in The Times
S
H
A
B
B
Y
More clues leading to the result SHABBY
- Worn out, quiet cat dropping head
- Despicable British bishop breaking silence, indeed
- Dirty books in second venue for literary festival
- Babe she gently rocked, keeping up appearances
- Coy about sailor being initially down at heel
- Mean parents finally going to hospital with sick baby
- Quiet religious house reportedly in poor condition
- Shameful attempt to steal answer books
- Unkempt, quiet kind of cat, with little time left
- Keep mum and baby terribly poor
Buddy explains!

The straight part
We know that "Dirty" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dirty = shabby.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 SHABBY mean?
SHABBY adjective- Torn or worn; unkempt.
- Clothed with ragged, much worn, or soiled garments.
- Mean; paltry; despicable.