How to correctly fork an open-source library? [closed]

What was the original license agreement? Your sentencing makes it confusing about whether the original part was GPL or you want to add GPL to it.

If the original license was GPL, then your new software must also be GPL. There is no way around it unless you get the permission from the author or all authors - if there is more than one. You can still sell your product if it is under GPL, but note that the buyer may 'resell' it with whatever price they find appropriate, including free, as long as license conditions are met. GPL is not a problem when building a website or software that is specific to a client, as long as you are fine with giving the client the rights to modify and republish the software.

But if you want to add GPL stuff to non-GPL project, then consider using LGPL license instead. LGPL allows to release the component itself under a GPL-like license while not requiring the other software to be GPL or LGPL in return.

It sounds like the two projects are incompatible. GPL is viral, adding GPL parts would require the library to be licensed under GPL, which may not be compatible with the original license. And the original license sounds like it requires the new (GPL) parts to be licensed under the original license too, which you don't have a right to do.

It sounds like you would be in breach of one or both licenses if you do what you want to do.