In order to edit the "Tour dates" section you have to open the Vamtam Builder (Guide to Vamtam Beaver Builder):
Click on the "Tour dates" section and edit the HTML element containing a script of the events from Bandsintown:
You can sign up and generate your own script here: https://manager.bandsintown.com/support/events-widget
If you don't want to use this script, you can install and activate the Events calendar, and the Event tickets plugins: