A reward that is promised to someone as an incentive to complete some task. It is a variant of "carrot and stick" or "carrot or stick," which refer to both reward and punishment being simultaneously offered/threatened as an incentive to complete a task. The boss offered a 10% bonus as a carrot on a stick to whomever sold the most units by the end of the month. I always allow myself a chocolate bar as a carrot on a stick to motivate me to go to the gym each day.