The most common and most likely answer to this crossword clue is the 7 plus 3 letter word FALLING OUT
I've seen this crossword clue in The Times
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More clues leading to the result FALLING OUT
Buddy explains!

The straight part
We know that "Leaving parade/disagreeing" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case leaving parade/disagreeing = falling out.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 FALLING OUT mean?
FALLING OUT noun- A rift between people or groups, often following a disagreement or quarrel
- A culture-bound syndrome primarily reported in the southern United States and the Caribbean, described as a constricted consciousness as a psychological response to anxiety and stress.