The most common and most likely answer to this crossword clue is the 6 letter word DICKEY
I've seen this crossword clue in The Daily Telegraph
D
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More clues leading to the result DICKEY
Buddy explains!

The straight part
We know that "Part of formal attire/not in good condition" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case part of formal attire/not in good condition = dickey.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 DICKEY mean?
DICKEY noun- A louse.
- Dicky dirt = a shirt, meaning a shirt with a collar.
- A detachable shirt front, collar or bib.
- A hat, especially (in the US) a stiff hat or derby, and (in the UK) a straw hat.
- A seat behind a carriage, for a servant.
- A seat in a carriage, for the driver.
- The luggage storage compartment of a sedan/saloon style car.
- A leather apron for a gig, etc.
- A small bird; a dicky-bird.
- (in negative constructions) An insignificant sound or thing; dicky-bird.
- A pilot.
- A hedge sparrow.
- A donkey.
- A haddock.
- Doubtful, troublesome; in poor condition