Is it possible to play with someone who lives far away on MCPE?

You can set up a server to play with each other. One user-friendly (and free) server hosting service is aternos.org. You must make an account for every server you host, but multiple accounts are allowed and you don't have to give your email. You may have to wait a minute or two after starting the server before you can join it. See their website for more details. Be sure to select Bedrock Edition when in prompts which software you want to use.

Edit: Another method suggested by @DisplayNameNotFound is to send a friend request to that player. I've never used this feature so I don't know how it works.