Hey Rich,
“Events” from the Events Calendar are registered as fairly-normal Post Types within WordPress – they’re of the “post” capability type, which means that you should have the basic “visibility” settings for an event in its edit screen.
Here’s a screenshot of these options, which start as just a line of text that says “Visibility: Public”, but expands to a few different options when you click that text (as shown here) → https://cloudup.com/cUBTc4eO6Ds
If you use any of those options – private or password-protected – they should work fine with Events. These are things that are default to WordPress itself, not The Events Calendar, so you can configure settings related to these options in your admin area’s general “Settings” tabs..
I hope this information helps! Let me know if it does.
Cheers,
George