The most common and most likely answer to this crossword clue is the 8 letter word CAPRIOLE
I've seen this crossword clue in The Times
C
A
P
R
I
O
L
E
More clues leading to the result CAPRIOLE
Buddy explains!

The straight part
We know that "horse jump" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case horse jump = capriole.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 CAPRIOLE mean?
CAPRIOLE noun- A leap that a horse makes with all fours, upwards only, without advancing, but with a kick or jerk of the hind legs when at the height of the leap.
- A leap or caper, as in dancing.
- To leap; to caper.
- To cause (one's mounted horse) to perform a capriole.