What do you sing out an Apple ID

If you create/use a new Apple ID, you will lose access to some of your data and the purchases made with your existing Apple ID. You might want to explain what problems you are having with your current ID to see if someone can make suggestions that will fix your current ID problems.

Apple ID - create a new.      

Apple ID – Create        

Apple ID - Could Not Create or Could Not Set Up iCloud message.    

All purchases made using an Apple ID are tied to the ID. Delete the ID and you will need to download them using your new ID. There have been posts by people who have contacted Apple Support and they were told that if you delete an ID associated with an email address, you can never reuse the email address for an Apple ID.   Make sure you sign out from the places in the 4th link before deleting the ID.

How to delete your Apple ID account.         

Apple ID – How to Delete.        

Delete Apple ID (new).         

What to do after you change your Apple ID or password - Apple Support      

I now see that you want to use a new Apple ID. But, still, you might want to consider the information below.

If you change your Apple ID, the old Apple ID will be gone.

Below is some basic information on changing your Apple ID. But read the whole document linked below. And you will need to go to your Apple ID account (appleid.apple.com) for additional information. 

See Change your Apple ID https://support.apple.com/en-us/HT202667. 

See this basic information:

1.   Sign out of iCloud on all of your devices, including your iPhone, Mac, Apple TV, and PC. If you use the Apple Music app on an Android device or use the Apple TV app a smart TV, sign out of those apps.

2.   Go to appleid.apple.com and sign in.

3.   In the Account section, choose Edit.

4.   Choose Change Apple ID.

You can sign out of iCloud on one of your devices, or you can sign out on all your devices to stop using iCloud (for sign out purposes, see 1 above). Before you sign out of iCloud, make sure that you archive or make copies of the information that you store in iCloud. When you sign out of iCloud, you can't access or use the following services on your devices or your Mac.

And see What to do after you change your Apple ID or password https://support.apple.com/en-us/HT204071