I set up my Apple Watch with an old iCloud and I do not know that information but I want to pair my Apple Watch with my new Apple ID

See if you can recover the ID/password. Use every email address you can think of.

Apple ID - How to find your Apple    An iCloud e-mail address is an Apple ID.

Apple ID - Find              

For the Apple ID password, enter the Apple (iCloud) ID and click Forgot Password. See if you can get an email option if necessary.

Apple ID - Manage            

Apple ID – Forgot Password