The most common and most likely answer to this crossword clue is the 8 plus 3 letter word CLIP-ONS (A)
C
L
I
P
-
O
N
S
(
A
)
Buddy explains!
The straight part
We know that "Hoof-beat encircles" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case hoof-beat encircles = clip-ons (a).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.