Exclusive
Exclusive is a term used in contracts to reference the terms of a licensing scenario. If something is exclusive it means it is only to be used within the context referenced & in no other way or for no other clients. Sometimes this is time-based, geography-based, or project-based.
Depending on the terms of exclusivity, it is appropriate to ask for more money, the more restrictions are tied to your ability to re-sell or promote your artwork.