Play offline on PS4 console

Sony didn't lie, you can play on PS4 without an internet connection.

Now, in the games, there are online and offline modes. It's obvious that you won't be able to play multiplayer without a connection. Well, that's just common sense; I don't know what else to tell you.

If you're looking for a good offline racing simulation game, then you'll get bored with Gran Turismo; it's really made for online play. Rather check out ACC, Assetto Corsa Competizione. Make sure to get the Competizione version, not the regular Assetto Corsa. In that game, you'll enjoy the career mode or creating your own races. The AI is really well done, and I promise you'll have some great battles as you raise its level. Personally, I have more fun having good fights against the AI in ACC than against clueless players online in GT who are just there to send you crashing into the scenery.