The most common and most likely answer to this crossword clue is the 12 letter word PROTESTATION
I've seen this crossword clue in The Daily Telegraph
P
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O
T
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S
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Buddy explains!
The straight part
We know that "Complaint" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case complaint = protestation.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 PROTESTATION mean?
PROTESTATION noun- A formal solemn objection or other declaration
- A declaration in common-law pleading, by which the party interposes an oblique allegation or denial of some fact, protesting that it does or does not exist, and at the same time avoiding a direct affirmation or denial.