This is a play of taking the reins of the horse from the hands of the player as you see drawn here. The scholar, when he closes with another horseman, rides to the right side and throws his right arm over the horse’s neck, takes the reins on the players left side with his overturned hand, and lifts the reins over the horses head. This play is safer in armour than unarmoured.
Here, you are not trying to injure your opponent, but capture their horse and lead them away. This is more for a melee situation where you will have a group of friends nearby, ready to subdue the rider. The horses will need to be moving slowly relative to each other for this to work.
As you approach each other, reach over the head of your opponents horse. As much as possible, keep your elbow in so as not to overstretch and unbalance yourself. You will need to lift the reins reasonably high so as to clear the horses head. The whole movement will need to be done smoothly and quickly so as to snatch the reins from your opponents grasp.
Turning your horse to the left, move off at speed as soon as the reins are clear. As you lead your opponent away, you do not want them to catch up to you. If they do, you will be at risk of them using the 1st scholar of horseback grappling against you. As you have one hand controlling your own horse, and the other controlling your opponents horse, you are in a potentially vulnerable position. For this reason, the play is safer to do when wearing armour.