The most common and most likely answer to this crossword clue is the 10 letter word SIDESADDLE
I've seen this crossword clue in Financial Times
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More clues leading to the result SIDESADDLE
- Subordinate to charge for riding aid
- Pages confuse the royal way of being “up”
- Teams go off the way one may go up
- Teams go off riding in unorthodox manner
- Team Blue note the French equestrian method
- How ladies rode interests designated driver taken in drink
- Duchess finally dies in agony – rotten way for a lady to go
- In tricky riding position Dad slides painfully on to earth
- Ladies on backs of horses rode round ground — disposed so?
- A theologian in Leeds is excited to see ladies riding up like this
Buddy explains!

The straight part
We know that "riding aid" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case riding aid = sidesaddle.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 SIDESADDLE mean?
SIDESADDLE noun- A saddle, usually for a woman, in which the rider sits with both legs on the same side of the horse.
- On, or as if on, such a saddle.