A rematch was a second contest between two athletes with the goal of giving the loser of the original match another chance to win.
In 2370, Doctor Julian Bashir was hesitant to have a racquetball rematch between himself and Miles O'Brien, citing the chief engineer's stressing over his earlier loss. Later, when Quark arranged a charity competition, with the proceeds to be given to the Bajoran Fund for Orphans, Bashir conceded to having a rematch, which O'Brien won. (DS9: "Rivals")