Enter the Apple (iCloud) ID and click Forgot Password.
Apple ID - Manage
Apple ID – Forgot Password
Are you signed into the App Store/iTunes with your new ID? Are you seeing the old ID when trying to do app updates? A request for another Apple ID password is often caused by updates to apps/purchases that were made when using the other ID. Those purchases are tied to the other ID and can't be transferred. One option is to delete the apps/purchases made by the other ID and download them using the new ID if desired. If necessary, check your purchases history to see which apps/purchases weren’t made by the current ID.
Purchase History Review