If you’ve granted someone a license to use your copyrighted work, and they violate the terms of the license, you may have a claim for breach of contract or copyright infringement. Which cause of action depends on the nature of the breach.
Let us assume that you licensed the other party to use the copyrighted work in print in exchange for monthly payments. The other party has stopped their monthly payments, but are still using the the work in print. They are currently in breach of the contract, and can be sued for the breach. They cannot be sued for copyright infringement until they are notified that, as a result of the breach, the license has been cancelled.
If, however, the other party has a license only for print use, but are using the work online, they are infringing your copyright, and could be sued immediately, assuming the work is registered.