The most common and most likely answer to this crossword clue is the 4 letter word YELP
I've seen this crossword clue in The Guardian
Y
E
L
P
Buddy explains!

The straight part
We know that "Cry out" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cry out = yelp.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 YELP mean?
YELP noun- An abrupt, high-pitched noise or utterance.
- A type of emergency vehicle siren sounding quicker and more intense than the wail.
- To utter an abrupt, high-pitched noise.