The most common and most likely answer to this crossword clue is the 11 plus 4 letter word SHORT-EARED OWLS
I've seen this crossword clue in Financial Times
S
H
O
R
T
-
E
A
R
E
D
O
W
L
S
Buddy explains!
The straight part
We know that "those that might give a hoot" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case those that might give a hoot = short-eared owls.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.