Does the sentence, "Charles is not only persistent, he is also driven to gain new knowledge" need a conjunction? Or is this a comma splice?
The sentence sounds grammatically correct as it stands. It doesn't have a comma splice, and it already has a conjunction.
A comma splice requires the parts on both sides of the comma to be complete (or main) sentences:
A comma splice, also called a run-on, occurs when a writer has connected two main clauses with a comma alone. A main clause makes a complete thought, so you should not find a wimpy comma struggling to join two such powerful clauses. - Grammar Bytes!
Although your quote doesn't include the word "but" before "also", the "Charles is not only ..., he is also ..." structure it uses is an acceptable variant.