Bearing Rein
A fixed strap which is fastened at one end to the bridle, at the other to the hook on the saddle pad. By its means the horse is prevented from dropping its head, and is made to appear more showy, and is said by some drivers to be better under control. A more severe form is known as the Gag bearing rein or Gag.
This strap is first attached to the headpiece, then taken through a swivel on the bridoon, and then goes to the hook on the pad.