What role does the following verse play after Paul teaches prayer about everything?
The next verse acts as the capstone on the teaching about prayer, concluding the idea of bringing anything and everything before the throne of grace even when God may answer no or not yet. It resolves the limbo left by that open-ended petitioning and completes the concept with a final word.
The speaker explains that after teaching we can come before the throne of grace with anything and everything, asking with thanksgiving for legitimate things, and expecting a yes, a no, or a maybe later, the next verse puts the cap on this whole concept. Even though God may say no or maybe later, which kind of leaves us in limbo, the next verse provides the concluding resolution. He directs attention to what that verse says as the final word on the matter.