The most common and most likely answer to this crossword clue is the 4 plus 5 letter word HOME RANGE
I've seen this crossword clue in The Times
H
O
M
E
R
A
N
G
E
Buddy explains!
The straight part
We know that "wild animal's domain" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case wild animal's domain = home range.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.