1. To come to a stop while riding a horse. Why don't we rein up over by that stream so the horses can get a drink? I reined up so I could listen for predators rustling around me.
2. To bring a horse to a stop by pulling back on its reins. In this usage, a noun or pronoun can be used between "rein" and "up." She reined her horse up, drew her bow, and fired an arrow straight into the center of the target. The bandits reined up their horses outside the front of the tavern and drew their firearms.
rein something up
to bring something, usually a horse, to a stop. She reined her horse up and stopped for a chat. Rein up your horse and stop for a while.
[for a horse rider] to stop. The equestrian reined up and dismounted. We all reined up and waited for the cars to pass by.