The most common and most likely answer to this crossword clue is the 4 letter word HAHA
I've seen this crossword clue in Financial Times
H
A
H
A
More clues leading to the result HAHA
Buddy explains!

The straight part
We know that "the cackling" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case the cackling = haha.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 HAHA mean?
HAHA interjection- An onomatopoeic representation of laughter.
- Type of boundary to a garden, pleasure-ground, or park, designed not to interrupt the view and to be invisible until closely approached.