How do I get HBO Max

I’m assuming you have an Apple TV box, and—since this isn’t a smart TV—are not using the Apple TV in the TV.

Add the HBO Max app to your Apple TV HD or Apple TV 4K.

https://www.reuters.com/article/us-media-streaming-hbo-max/hbo-max-streaming-service-will-be-available-on-apple-devices-at-may-27-launch-idUSKCN2292I7

If you do not have an Apple TV box, then you can use AirPlay 2 from another Apple device, if your TV supports AirPlay 2.

If your TV doesn’t support either AirPlay 2 or the Apple TV app, you’ll probably be looking for an Apple TV box.