The most common and most likely answer to this crossword clue is the 7 letter word WOLFMAN
I've seen this crossword clue in The Guardian
W
O
L
F
M
A
N
More clues leading to the result WOLFMAN
Buddy explains!

The straight part
We know that "monster" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case monster = wolfman.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.