Hey Christine,
Thanks for reaching out to us!
Is this a one time transfer of all events from one site to another? If so, you can use the traditional WordPress Export/Import functionality. You can navigate to “Tools” -> “Export” on your current site and then import them into your new site by navigating to “Tools” -> “Import” and following the steps for importing data from another WordPress install.
However, if you’re looking for a constant syncing between two sites where new events added to one are automatically displayed on the second, this isn’t something that is currently possible with The Events Calendar. If you would like, you can log a feature request for this type of functionality here. Our developers can then evaluate the possibility of including this feature in a future release.
For limited functionality, there is an RSS feed that is generated for events that could be used to display the events on the second website. It is limited in the data that is displayed but could add a bit of automation to the process.
Let me know if this helps.
Thanks!