Bought a new Apple Watch and cannot unpair the prior one.

What do you mean by "prior one"? Your can't remove your other watch? You can't remove the Activation Lock on the new watch?

Here are two ways to unpair your older watch besides using the paired iPhone:

• See the 'How to erase your Apple Watch if you don't have your iPhone' section of:

Unpair and erase your Apple Watch - Apple Support

• With a web browser, go to: https://www.iCloud.com and sign in with your Apple ID. Open Find My iPhone and select All Devices (at the top). Then click your Apple Watch, select 'Erase Apple Watch', and select Next until the device is erased. Finally click "X" next to remove your Apple Watch.

Activation Lock is designed to prevent anyone else from using an Apple Watch if it's ever lost or stolen.

About Activation Lock on your Apple Watch - Apple Support

Activation Lock is an anti-theft feature that cannot be bypassed. Only the previous owner can remove the lock by using their Apple ID & password. Apple will not help you find the previous owner. If the previous owner cannot or will not remove the lock, then the watch is useless to you or anyone else. Try to get a refund (through eBay) or dispose of the watch properly. In the future, see the 'Before you buy a watch from a third-party' section in:

What to do before you sell, give away, or trade in your Apple Watch, or buy one from someone else - Apple Support

To unpair and erase watch and remove Activation Lock

From a web browser,sign in to iCloud.com with your Apple ID.

Go to Find iPhone.

Click All Devices at the top of the screen.

Click your Apple Watch.

Click Erase [device]. Select Next until the device is erased.

Click Remove from Account.