Whilst the email account used to identify your AppleID account may no longer exist (the email address being used as the “username” that identifies your AppleID account) you should still be able to recover your credentials.
Your AppleID credentials can be recovered here:
https://iforgot.apple.com
To recover your credentials, you’ll need access to any one of the following:
- Your primary email address mailbox that corresponds with your AppleID
- Any of the secondary/recovery email addresses that should be configured for your AppleID account
- Any of the trusted telephone numbers (fixed line or Cellular/Mobile) that are associated with your AppleID
Unless you AppleID account has not been fully/correctly configured, or has been seriously neglected, recovery of the AppleID and password should not be difficult.
More information about recovery of your AppleID:
If you forgot your Apple ID - Apple Support
More information about recovery of your AppleID password:
If you forgot your Apple ID password - Apple Support
When you recover access to your credentials, you would be well advised to log-in to your AppleID account from a web browser - and verify/update any email addresses and trusted telephone numbers:
https://appleid.apple.com