All versions of The Last of Us 1 have New Game Plus. This is unlocked after you complete the campaign, and is selectable from the New Game menu. In all editions of the game, your Weapons Upgrades will transition between playthroughs and your collectibles will not.
However, The Last of Us: Part I (PS5, PC) includes an additional toggle between the following two modes:
Full Loadout: Play through the game again with all weapons, upgrades, and recipes obtained in a previous playthough. Weapons and recipes unlock when Joel retrieves his backpack in Boston.
Classic: Only upgrades carry over from a previous playthrough. Weapons and recipes unlock on progression.
If you're playing The Last of Us Remastered (PS4) or The Last of Us (PS3) then you can only use the Classic option described above. You'll also be restricted to the highest difficulty setting you completed the campaign on, whereas in The Last of Us: Part I you'll have the flexibility to choose any of the available difficulty settings.