The most common and most likely answer to this crossword clue is the 11 letter word REMONSTRATE
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The straight part
We know that "Protest" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case protest = remonstrate.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 REMONSTRATE mean?
REMONSTRATE verb- To object; to express disapproval (with, against).
- Specifically, to lodge an official objection (especially by means of a remonstrance) with a monarch or other ruling body.
- (often with an object consisting of direct speech or a clause beginning with that) To state or plead as an objection, formal protest, or expression of disapproval.
- To point out; to show clearly; to make plain or manifest; hence, to prove; to demonstrate.