/ˈpɒstrɔːrs/ or /ˈpɒstrɔːrs/ is not found, but post- or post-rose or post-horse are possible

Definitions

1. noun

a post or monument marking the site of a former horse or a point of interest

“The traveler stopped at the postrorse to take a photo of the historic landmark.”

2. noun

a post or monument marking the site of a former horse, especially a post marking the site of a former horse’s grave or the place where it died

“The postrorse stood proudly in the field, serving as a reminder of the horse’s life and legacy.”