Re: Battlefield 4 premium purchased but can't play after EA Play subcription end.

You do need to sign up and pay for having an ongoing subscription service active for your account, to play this online multiplayer game.

You may have purchased the game itself, which I think still should give you access to the single-player campaign part of it, but you cannot play in the multiplayer environment without also paying for the ongoing subscription for access to the online multiplayer environment.