I want to delete an old watch

Without knowing what exactly hoppens or does not happen when your try to pair the new watch see:

If you can't pair an Apple Watch with your iPhone - Apple Support

What OS version is on the phone?

What model new watch? You need a minimum phone OS verion for watchs and version is specific to the model watch.

• for the new phones: Apple Watch Ultra, Apple Watch Series 8, and Apple Watch SE require an iPhone 8 or later with iOS 16 or later.

Then;

Set up and pair Apple Watch