The most common and most likely answer to this crossword clue is the 12 letter word REMONSTRANCE
I've seen this crossword clue in The Daily Telegraph
R
E
M
O
N
S
T
R
A
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More clues leading to the result REMONSTRANCE
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 = remonstrance.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 REMONSTRANCE mean?
REMONSTRANCE noun- A remonstration; disapproval; a formal, usually written, objection or protest.