If the old account has been properly deleted then it cannot possibly have a subscription running on it. Are you sure you didn't start a subscription with a third party? That will have nothing to do with Apple.
This support article explains how to cancel a subscription from Apple on various kinds of hardware and online ➔ https://support.apple.com/118428 Use the drag-down menu to choose the kind of equipment you have.
Notes:
• “If you signed up for a trial subscription and you don't want to renew it, cancel it at least 24 hours before the trial ends.” Exceptions in: https://support.apple.com/108098
• Free trials will usually automatically turn into paid subscriptions unless you cancel in time.
• Many subscriptions are set to renew automatically until you intentionally cancel them.
• If you don’t see Cancel Subscription, then the subscription is already canceled and won't renew. An "Expires" date (instead of "Renews") means the current subscription has been canceled but will work until the expiration date. "Resubscribe" (or Renew) is just in case you change your mind about having it end.
• Deleting an app does not cancel a subscription.
You can view your subscriptions here —> https://apps.apple.com/account/subscriptions (requires sign-in)
If you can’t find the subscription that you want to cancel, click here —> https://support.apple.com/118428?device-type=mac#:~:text=canceled%2E-,If%20you%20can%27t%20findnd and review the possibilities:
- Charges for Family Sharing members or additional Apple Accounts you may have will not appear when you are signed into your Apple Account. Search for email “receipts from Apple” or “ invoices from Apple” and get the account names. Issues have to be resolved when signed in with the other account. If using Family Sharing and viewing purchase history under Report A Problem [ https://reportaproblem.apple.com/?s=6 ], make sure the “Apple Account” box is set to “All”.
- Subscriptions made directly with a third party. More about this here —> https://support.apple.com/118126 and here —> https://discussions.apple.com/thread/256248657?answerId=261844889022&sortBy=oldest_first#261844889022
- Linking missing AppleCare plan subscriptions —> https://support.apple.com/102190#linking
If you still can't find a subscription or still have problems, contact Apple Support for your account country ➔ https://support.apple.com/HT201232 (Telephone numbers will often only work when called within-country.)