If you’re on the Store page for the PS4 version of the game, you should see the below with a link to the PS5 version on the right side. Press on that:
Once you’re taken to the page for the PS5 version, or if you’re already there, you should see the option to buy the upgrade for $15. If you don’t, double-check you’re on the right PSN account:
Once you’ve paid the upgrade fee, the checkout screen should prompt you to download the game. Alternatively you’ll find it in your library with the PS5 version as an option to download.
Upgrading A Physical PS4 Copy Of The Last of Us Part 2
Insert your physical PS4 disc for The Last of Us Part 2 (you’ll need a PS5 console with a disc drive, naturally)
Follow the above steps, as long as you have the disc in the process should be the same
Once you’ve bought the game at the $15 upgrade price and installed it, you can play – but you’ll need to keep that original disc and have it inserted in the console any time you want to play the PS5 version, so don’t get rid of it!