How do I disable "link preview" in iOS safari?

Go to Settings > General > Accessibility > 3D Touch and either turn off 3D Touch (this disables the link previews entirely) or adjust the sensitivity to require a harder press so you don’t unintentionally trigger it.

The feature is activated by how hard you press, not how long you press and hold. Even with it turned on, you can still press and hold lightly to select text and get the normal menu with copy and other options.

I think the other answer is outdated. Link preview is the default action on long-press now (not just 3d touch), and not just in Safari.

To disable it, long-press a link and tap the "Hide preview" option. That option is currently found in the top right corner (which might change with future updates).

To increase the time it takes to activate a long-press under iOS 14, go to Settings -> Accessibility -> Touch -> Haptic Touch and change it from Fast to Slow.