The most common and most likely answer to this crossword clue is the 7 letter word MARCHED
I've seen this crossword clue in The Sunday Telegraph
M
A
R
C
H
E
D
More clues leading to the result MARCHED
Buddy explains!

The straight part
We know that "took part in moving protest" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case took part in moving protest = marched.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 MARCHED mean?
MARCHED verb- To walk with long, regular strides, as a soldier does.
- To cause someone to walk somewhere.
- To go to war; to make military advances.
- To make steady progress.
- To have common borders or frontiers