When Projector launches, it will automatically let you know when there is a new version available in the App Store:
Clicking Update Now will take you to the App Store page for Projector so that you can upgrade the app. Clicking Later will dismiss the alert and allow Projector to continue running.
The alert also lets you know when the current version of the app will no longer be supported. If you have not used Projector in a while and it's currently running an older, unsupported, version, then you will need to upgrade the app to continue using it:
Clicking Update Now will take you to the App Store page for Projector to upgrade. The current Projector app will also logout.