Purchased Apps are forever tied to the AppleID account from which they are purchased. To download or update an App, you must be signed-in to the Apple App Store with the correct AppleID. Presumably you have stopped using your original AppleID account - and have since used a different account with your iPad...
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.
If the original AppleID account has been deleted - as suggested by your post - you will not be able to recover the AppleID account or any purchased Apps that were associated with it. In such circumstances, your only option is to delete the App(s) that cannot be updated from your iPad - after which you can re-download the Apps using your current AppleID. You should note that for "paid" Apps, they will need to be purchased again.