Save Minecraft PE savegame?

I have Minecraft on my Nexus 9 (Android 7). Since this but has lately more and more dropouts or crashes (is no longer the youngest), I'm considering to purchase a new device. Which one I do not know yet, but it definitely should have Android. Is there a way to save the Minecraft PE save game with no root or bring it to the new device?

Maybe with a phone backup. At Apple, that's possible, but I do not know about Android. Unfortunately, there's no easy solution otherwise. I find that very difficult.