Hey there Diana!
Thanks for reaching out — that’s a great question, I can help with that 🙂
Though this isn’t a feature that is built into The Events Calendar, it can be added for sure.
First, using our Themer’s Guide you’ll want to create a link or button that can be used to reset the search field. You could attach that to a reset button with the onclick attribute, or even better you can use jQuery (first example in this link).
The JS code to be triggered would look like →
jQuery('#tribe-bar-form').tribe_clear_form();
Hope that helps!