Warzone is a completely free to play game on PlayStation, which means you don't need PS Plus to play Call Of Duty Warzone.
Playing Call of Duty Warzone on PS will only require you to have a PlayStation Console and a PSN account. If these two boxes are checked, you can play Warzone online like other online games without a paid subscription. Moreover, not only it works like that on every platform, but you should know Call of Duty Warzone is cross-platform, so you can play it with your PC and Xbox friends as well with your best m13b loadouts!
Will Activision Move Warzone to PS Plus?
It's very unlikely that Activision will ever require Call of Duty Warzone to have a PS Plus subscription. Look, the game is competing with titles like Fortnite and Apex Legends, and these will always be free-to-play, and in my opinion, this alone is a good reason to think that the game will stay free forever. By adding Warzone to PS Plus, the game would most likely lose a big amount of their player base, as casual players would most likely switch to other battle royale titles.
Is Call of Duty: Modern Warfare Required to Play Warzone on PlayStation?
No, you don't need to have Call of Duty: Modern Warfare to play Call of Duty Warzone on PlayStation or desktop.
On the other hand, we should point out that you will need an active PS Plus membership to play Call of Duty: Modern Warfare. As Modern Warfare is not a free-to-play title, and just like on PC, you are allowed to play the game on PlayStation Consoles by paying a certain fee.
The link between these two games has some key points and advantages. For example, all of your equipment in Modern Warfare is automatically unlocked in Call of Duty Warzone game, and you can customize your weapon drop-ins so that you can request an airdrop of your favored weapon, giving you the upper hand over other players.