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Related to bearing rein: checkrein
A rein for a horse; a checkrein.
(Horse Training, Riding & Manège) chiefly Brit a rein from the bit to the saddle, designed to keep the horse's head in the desired position. Usual US word: checkrein
1. a short rein passing from the bit to the saddle of a harness to prevent the horse from lowering its head.
2. a short rein joining the bit of one of a span of horses to the driving rein of the other.