The most common and most likely answer to this crossword clue is the 9 letter word DENIGRATE
I've seen this crossword clue in The Daily Telegraph
D
E
N
I
G
R
A
T
E
More clues leading to the result DENIGRATE
- Slight gradient, unusual direction
- I fret at the bottom of haunt that's run down
- Belittle lad with one good grade
- To belittle and head off Biden’s reform, strike a false note
- Blacken as one occupying room with fireplace
- Damage the reputation of dubious diet range
- Knock hole at the front of one jar
- Run down gradient exploding with energy
- Maybe jeans male leaves by fireplace to blacken
- Slight gradient marred end of ramble
Buddy explains!

The straight part
We know that "Run down" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case run down = denigrate.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 DENIGRATE mean?
DENIGRATE verb- To criticise so as to besmirch; traduce, disparage or defame.
- To treat as worthless; belittle, degrade or disparage.
- To blacken.