Sign into the old account an make sure iCloud is activated in Settings.
Typically an Apple ID is an email address you have used.
Click on this link to read about ways to find your Apple ID --> If you forgot your Apple ID email address or phone number - Apple Support
or go directly to this link --> https://iforgot.apple.com/password/verify/appleid#
If you still need help:
Contact Apple for help with Apple ID account security "This article provides country-specific Apple Support contact information for customers seeking help with their Apple ID password or other security-related issues."
Contact Apple for help with Apple ID account security - Apple Support
Also look in Keychain, and in a browser's security settings if you use it to automatically sign into Apple when using a browser.