The most common and most likely answer to this crossword clue is the 6 letter word SOMBRE
I've seen this crossword clue in The Times
S
O
M
B
R
E
More clues leading to the result SOMBRE
- Gloomy brother in certain unspecified surroundings
- Bury unevenly in a little grave
- With new leader, man becomes sad
- Dim doctor lancing boil perhaps
- Rose rambling over doctor’s grave
- Most of broad hat is dark
- Grey hat tipped or removed
- melancholy
- Serious doctor absorbed by wound?
- Gloomy American’s angry about graduate physician
Buddy explains!

The straight part
We know that "Dim" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dim = sombre.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 SOMBRE mean?
SOMBRE noun- Gloom; obscurity; duskiness.
- To make sombre or dark; to make shady.
- Dark; gloomy; shadowy, dimly lit.
- Dull or dark in colour or brightness.
- Melancholic, gloomy, dreary, dismal; grim.
- Grave; extremely serious.