The most common and most likely answer to this crossword clue is the 4 plus 6 letter word NEAR MISSES
I've seen this crossword clue in The Guardian
N
E
A
R
M
I
S
S
E
S
More clues leading to the result NEAR MISSES
Buddy explains!
The straight part
We know that "just avoided accident/s" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case just avoided accident/s = near misses.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.