I just got a new Ipad Air 3. I have an IPhone XR. I would like to sync a game app from my phone to my Ipad, so I can play the same game on either device. How do I do this?

It depends on the app, some can be synced, some are independent on each device.

Generally:

• Log in using the same Apple ID on both devices;
• Use the same Game Center (in Settings) account/nickname, if you turned GC to ON;
• If the game uses its own account login and password, use the same one everywhere.

Have you checked that the game is available on both devices?

Not all apps are compatible on iPhone and iPad