The most common and most likely answer to this crossword clue is the 7 letter word STABLED
I've seen this crossword clue in Independent
S
T
A
B
L
E
D
Buddy explains!

The straight part
We know that "Kept horses" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case kept horses = stabled.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 STABLED mean?
STABLED verb- To put or keep (an animal) in a stable.
- To dwell in a stable.
- To park (a rail vehicle).
- Kept or located in a stable
- (of a rail vehicle) parked