Drafting: consensus that notice includes prior
From the comments and from my own queries, I have found a consensus: the concept of "prior" is inherent in "notice."
Generally, we agree that it would not be reasonable in a typical transaction to require notice that is not in advance. If you want to make an exception from that generality, specify it.
Several commenters and others also pointed out that requiring only "prior" notice will often be inadequate: you should specify how prior. Ten days? Thirty days? Otherwise you leave your client open to an argument that notice can be given one minute before the event, or you send your client to a court or arbitrator to decide what time period would be reasonable.