The most common and most likely answer to this crossword clue is the 10 letter word INCIDENTAL
I've seen this crossword clue in The Guardian
I
N
C
I
D
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A
L
More clues leading to the result INCIDENTAL
- & 28 Scene and dubious claim about us – it creates mood
- Concerned with teeth, after front teeth half removed by accident
- Auxiliary volunteers inclined to wander around outside
- Fortuitous identical moves trapping knight
- Note inserted in otherwise identical sort of music
- Happening almost entirely to be describing theatre music?
- Subordinate in police dept to go on hire, topless
- Accompanying cool revolutionary in charge of chopper
Buddy explains!

The straight part
We know that "by accident" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case by accident = incidental.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 INCIDENTAL mean?
INCIDENTAL noun- Minor items, not further defined. Incidental expense.
- Something that is incidental.
- Loosely associated; existing as a byproduct, tangent, or accident; being a likely consequence.
- Occurring by chance
- (of radiation) Entering or approaching, prior to reflection (more frequently incident).