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:

If you don't want to use this script, you can install and activate the Events calendar, and the Event tickets plugins:

Vamtam Beaver Theme: Guide to The Events Calendar Plugin

Vamtam Beaver Themes: Guide to Event Tickets Plugin