If you're looking for anime similar to Uma Musume: Pretty Derby - BNW no Chikai, you might like these titles.
Follows Jungle Pocket, who wishes to participate in the Triple Crown Classic race, which can only be run once in a lifetime. She faces rivals Agnes Tachyon and Manhattan Cafe.
Set in the year 20XX, when a woman won the Japan Derby for the first time, it lead to a big change in the image for the sport, with many girls wanting to become jockeys, and many girls enrolling in jockey schools with the aim to win the Japan Derby, Tenno Shou, Arima Kinen, Prix de l'Arc de Triomphe, and other races.
The jockey curriculum at the Horse Racing School... A school with incredibly difficult entrance requirements, where only one out of every ten to twenty applicants is accepted, and students need not just book smarts, but also physical and athletic abilities. There, a boy who is a popular idol meets his real dream for the first time. A boy who grew up on an island dreams of spending his days racing with horses. A boy from England is unsure of the path his parents have chosen for him, but still chooses to follow his dreams. This is a story about boys who pursue their dream of becoming a jockey.