The most common and most likely answer to this crossword clue is the 8 letter word GRAVAMEN
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The straight part
We know that "most serious part of complaint" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case most serious part of complaint = gravamen.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 GRAVAMEN mean?
GRAVAMEN noun- The grievance complained of; the substantial cause of the action; also, in general, the ground or essence of a complaint.