We have a question here called So the GPL doesn't restrict the creator of the software in any way? which addresses the first part of this issue. Essentially, as long as you are the sole rightsholder in this library (ie, it's not GPL because it's based on somebody else's GPL code) then it is fine for you to convey the library to the client on terms other than straight GPL, eg on terms that permit proprietary usage.
But having clarified the terms that don't apply to the library, it is perhaps more important that you clarify those that do. The usual arrangement when Alice pays Bob to write code for her is that Alice will expect to hold the copyright on the work as delivered, so that she can use it as she pleases. But if you were to do this, then you could no longer distribute the library under GPL, since you would have no rights to do so.
It will therefore be important to address exactly what rights the payer is getting, since they will need to be able to do all the things they intend to do with the code they've paid for (eg: copy it, use it, sell it, relicense it, etc.) without taking from you the rights to do what you want to do with the library (continue to distribute it under GPL). This will require a negotiation process between you and the client, and it would probably be a good idea to get your lawyer involved.