Note: Please make sure that you activated The Events Calendar and built data in Events section prior to implementing steps stated below.Seek more related information via these links:
To achieve an Event item in header menu, please follow these steps:Step 1: Navigate to Events > Settings > Display > opt Default Events Template in Events template > Save changes
Step 2: Go to Appearance> menu > click the triangle of Event Categories on the left side.
Step 3: Tick Event box and click Add to Menu then Event item will appear in Menu area on the right side
Learn more about setting up Header Menu: