The most common and most likely answer to this crossword clue is the 6 plus 6 letter word LIVERY STABLE
I've seen this crossword clue in The Sunday Telegraph
L
I
V
E
R
Y
S
T
A
B
L
E
Buddy explains!
The straight part
We know that "Equestrian business" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case equestrian business = livery stable.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.