Between indie games and AAA titles, there are a ton of good Playstation 4 strategy games available for your PS4. Many people cite SteamWorld Heist as the best PS4 strategy game, a follow up to SteamWorld Dig but with a larger focus on turn-based strategy. PS4 games in the strategy genre also include the critically acclaimed Invisible, Inc, as well as Banner Saga, Valkyria Chronicles Remastered, and much more.
If you own a Playstation 4 and have played many of these turn-based strategy games, vote up the titles you would recommend to other PS owners. Downvote games that you played but didn't love, but only if you actually have experience with the title.