Yes, you can reuse the essays from your National College Match application for the Common App. Please ensure your response fits the given prompt, and keep the word limit in mind.
However, please note that some schools will require a school-specific supplement that includes writing responses, which should not be recycled from your QuestBridge application. Should you become a Finalist, the schools will provide further information about these supplements. You can find details about school-specific requirements under the Application Requirements tab on a specific college partner's page.