If I turn and turn off my sky q box, but will I lose the new sky sports plus app

No, turning your Sky Q box on and off will not cause you to lose access to the Sky Sports app or any of your existing apps. The apps installed on your Sky Q box are tied to your account rather than the state of the box itself. As long as your subscription to Sky Sports is active and your account is in good standing, you should be able to access the Sky Sports app after restarting the box. If you do encounter any issues, you may need to log back into the app or check for updates.