The most common and most likely answer to this crossword clue is the 13 letter word HIDE-AND-SEEK
I've seen this crossword clue in Independent
H
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More clues leading to the result HIDE-AND-SEEK
Buddy explains!

The straight part
We know that "hunting around" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case hunting around = hide-and-seek.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 HIDE-AND-SEEK mean?
HIDE-AND-SEEK noun- (games) A game where the players have to hide and one has to seek them out.