The most common and most likely answer to this crossword clue is the 7 letter word FORELEG
I've seen this crossword clue in Financial Times
F
O
R
E
L
E
G
Buddy explains!

The straight part
We know that "a /bit/ of a beast" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a /bit/ of a beast = foreleg.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 FORELEG mean?
FORELEG noun- Either of the two legs towards the front of a four-legged animal, a piece of furniture, etc.