When you remount a bicycle or horse, you get back on it after you have got off it or fallen off it. He was told to remount his horse and ride back to Lexington The pony scrabbled up and waited for the rider, who remounted and carried on. to get onto a horse, bicycle etc again
a fresh horse especially (formerly) to replace one killed or injured in battle provide with fresh horses; "remount a regiment" mount again, as after dissembling something mount again; "he remounted his horse
The opportunity of, or things necessary for, remounting; specifically, a fresh horse, with his equipments; as, to give one a remount