The most common and most likely answer to this crossword clue is the 7 letter word SOOTIER
I've seen this crossword clue in The Daily Telegraph
S
O
O
T
I
E
R
Buddy explains!

The straight part
We know that "dirtier" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dirtier = sootier.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 SOOTIER mean?
SOOTIER adjective- Of, relating to, or producing soot.
- Soiled with soot
- Of the color of soot.
- Dark-skinned; black.