The most common and most likely answer to this crossword clue is the 6 letter word TANNED
I've seen this crossword clue in The Daily Telegraph
T
A
N
N
E
D
Buddy explains!

The straight part
We know that "Brown" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case brown = tanned.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 TANNED mean?
TANNED verb- To change to a tan colour due to exposure to the sun.
- To change an animal hide into leather by soaking it in tannic acid. To work as a tanner.
- To spank or beat.
- Having a suntan.
- (of leather) Finished, made using tannic acid (as opposed to abrasion).