The most common and most likely answer to this crossword clue is the 6 letter word MEWING
I've seen this crossword clue in The Daily Telegraph
M
E
W
I
N
G
More clues leading to the result MEWING
Buddy explains!

The straight part
We know that "making high-pitched cry" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case making high-pitched cry = mewing.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 MEWING mean?
MEWING verb- To shut away, confine, lock up.
- (of a bird) To moult.
- (of a bird) To cause to moult.
- (of a deer) To shed antlers.
- (of a cat, especially of a kitten) To meow.
- To flatten the tongue against the roof of the mouth for supposed health benefits.
- The act of producing a mew sound.