The most common and most likely answer to this crossword clue is the 8 letter word COURSING
I've seen this crossword clue in The Daily Telegraph
C
O
U
R
S
I
N
G
Buddy explains!

The straight part
We know that "illegal hunting" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case illegal hunting = coursing.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 COURSING mean?
COURSING verb- To run or flow (especially of liquids and more particularly blood).
- To run through or over.
- To pursue by tracking or estimating the course taken by one's prey; to follow or chase after.
- To cause to chase after or pursue game.
- The sport of chasing wild animals, especially hares, with dogs by sight rather than by scent