How can i unlock my old iPad with a new Apple ID?

It's not asking for the email account's password. It's asking for the Apple ID's password. Might be the same text string, but they are not related or connected. And access to the old email account is not required at all.

If you updated your existing Apple ID on another device to a new email address, you don't need to do anything. Just enter the password for your Apple ID and it should unlock the iPad. Once it connects to the internet it will update the Apple ID to the new email address automatically. You don't need access to the old email address for this. Just the password for the Apple ID.

If you did in fact create an entirely new Apple ID, then you will need to first log in to the iPad and then sign out of the old Apple ID and sign in with the new one.

If you don't remember the password for the old Apple ID, then you will need to use Apple's iforgot service to try to reset it. You may need to contact Apple Support directly and use Account Recovery to reset the password since you no longer have access to that email address that Apple account is using to get the reset emails.

click here ➜ How to use account recovery when you can’t reset your Apple Account password - Apple Support

An AppleID account is intended to be used for life. If you need to change the primary email address that identifies your account, or your secondary (recovery) email addresses or trusted telephone numbers, you simply need to update your AppleID account as necessary.

Change your Apple ID - Apple Support

Change your Apple ID password - Apple Support

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

Change, add, or remove Apple ID payment methods - Apple Support

Few of us will have the luxury of forever keeping the same email addresses or telephone numbers - sometimes these needing to be changed for a variety of reasons. However, updating our AppleID account, maintaining access to our data and purchases, is easy and relatively straightforward - accommodating life’s many changes as they occur. Using a completely different AppleID account can introduce many complications and issues, not limited to losing access to paid Apps, subscriptions and services - these being forever tied to the AppleID account from which they were purchased.