The most common and most likely answer to this crossword clue is the 4 plus 8 letter word HUNT SABOTEUR
I've seen this crossword clue in Financial Times
H
U
N
T
S
A
B
O
T
E
U
R
More clues leading to the result HUNT SABOTEUR
Buddy explains!
The straight part
We know that "Animal activist" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case animal activist = hunt saboteur.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.