The most common and most likely answer to this crossword clue is the 4 letter word KLEE
I've seen this crossword clue in The Times
K
L
E
E
More clues leading to the result KLEE
Buddy explains!

The straight part
We know that "Swiss painter" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case swiss painter = klee.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.