An exclusivity agreement is a contract that two parties enter into to sell and stock each other's products or services and to promote them on an exclusive basis. There are many exclusivity agreements in corporate sponsorship and in retail agreements such as the right to sell one kind of beer in a bar or one brand of chips. This is a regular contract where if either party breaks the agreement they will be expected to financially recompense the other party for losses incurred from lost opportunity.
Justipedia explains Exclusivity
Exclusivity agreements also exist within sports sponsorship scenarios where a sports person who is hired to represent a company, such as Tiger Woods and Nike, will make an exclusivity agreement to never be seen during a game in anything other than the sponsor's brand. This can also extend to beyond the sport and the expectation that the sponsor will not ever be seen to be buying or using a competitor's brand.