The most common and most likely answer to this crossword clue is the 4 plus 5 plus 6 letter word DAME LAURA KNIGHT
I've seen this crossword clue in The Guardian
D
A
M
E
L
A
U
R
A
K
N
I
G
H
T
Buddy explains!
The straight part
We know that "British artist" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case british artist = dame laura knight.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.