If your app still says HBO Max, you'll need to download the updated Max app, but you won't have to pay for a new subscription.
If you have HBO through a cable/satellite/internet ... All you need to do is download the Max app on a supported device (more on those later), and simply sign in through your provider.
These days, it's Max -- not HBO Max -- that delivers HBO to the streaming masses. The service is home to popular shows like Succession, The White Lotus, Hacks and The Sex Lives of College Girls.