The most common and most likely answer to this crossword clue is the 7 letter word PARADES
I've seen this crossword clue in The Daily Telegraph
P
A
R
A
D
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S
More clues leading to the result PARADES
Buddy explains!

The straight part
We know that "Demonstrations" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case demonstrations = parades.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 PARADES mean?
PARADES noun- An organized procession consisting of a series of consecutive displays, performances, exhibits, etc. displayed by moving down a street past a crowd of spectators.
- A procession of people moving down a street, organized to protest something.
- Any succession, series, or display of items.
- A line of goslings led by one parent and often trailed by the other.
- Pompous show; formal display or exhibition; outward show (as opposed to substance).
- An assembling of troops for inspection or to receive orders.
- Posture of defense; guard.
- The ground where a military display is held, or where troops are drilled.
- A public walk; a promenade; now used in street names.
- (collective) (uncommon) A term of venery denoting a herd of elephants on the move.
- To march in or as if in a procession.
- To cause (someone) to march in or as if in a procession; to display or show (something) during a procession.
- To exhibit in a showy or ostentatious manner.
- To march past.
- To march through or along; (of a vehicle) to move slowly through or along.
- To assemble to receive orders.
- To assemble (soldiers, sailors) for inspection, to receive orders, etc.
- (of geese and other waterfowl) To march in a line led by one parent and often trailed by the other.