When a person issues a challenge to someone, they invite that person to take up a task or participate in a competition. However, there are different ways to express this action using different synonyms. Some alternatives could be to offer a dare, propose a contest, extend a rivalry, provide an incitement, present a provocation, or even present a gauntlet. Each of these options conveys the notion of challenging someone in different ways, but all express the same overall intention: to invite and motivate someone to take on a difficult task or engage in a competition. Choosing an appropriate synonym for "issues a challenge to" can help to add depth and variety to your writing and communication skills.