The ZeroTier menubar app is a separate process from the system service that makes ZeroTier work. You can quit the menubar app from it’s menu and the system service will continue to run.
To stop/start the ZeroTier system service, open Terminal.app and paste these commands:
sudo launchctl unload /Library/LaunchDaemons/com.zerotier.one.plist
sudo launchctl load /Library/LaunchDaemons/com.zerotier.one.plist