This Seeking Tech guide will explain how you can upgrade from the PS4 version of Horizon Zero Dawn to Horizon Zero Dawn Remastered on PS5.
If you have the PS4 version on the main menu screen, then you should be able to find the upgrade option on the bottom right.
If you don’t have the PS4 version on the main menu, then you need to go to Game Library. Afterwards, select Your Collection and then Horizon Zero Dawn. Select any version and you should be able to find the upgrade option on the right side of the product page.
Alternatively, you can go to the PlayStation Store. From there, you can search for Horizon. You should then be able to find the upgrade option from the search results page.