Well according to PS4 Upgrade Campain ending. It appears your account would have already been converted from a PS3 to a PS4 account.
As thanks to our players for supporting FINAL FANTASY XIV, we are automatically upgrading licenses for the PlayStation®3 version to the PlayStation®4 version. We hope players will take this opportunity to upgrade and enjoy fantastic new adventures in the realm of Eorzea.
Login to the Mog Station to verify that has occurred. If so, then you should be able just to install and run the game on your PS4 and log in with your FF account.