The most common and most likely answer to this crossword clue is the 4 plus 8 letter word PIET MONDRIAN
P
I
E
T
M
O
N
D
R
I
A
N
Buddy explains!
The straight part
We know that "Artist" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case artist = piet mondrian.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.