The most common and most likely answer to this crossword clue is the 12 letter word ILL-ASSORTED
I've seen this crossword clue in The Times
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More clues leading to the result ILL-ASSORTED
Buddy explains!

The straight part
We know that "Incompatible" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case incompatible = ill-assorted.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 ILL-ASSORTED mean?
ILL-ASSORTED adjective- Badly matched, or unmatched.