how do I get rid of an old apple id

My father has an older iPhone that was given to him by a relative that is no longer with us. There is an old apple id stuck that the phone keeps defaulting to whenever we try to update an app. Even though we have created, and signed on using a new apple id, the phone won't let us proceed with updates because the old id keeps popping up requesting the password. There is no way to recover the old password, because the old email address that it is tied to doesn't exist any longer. How can I make it so the phone no longer looks at / for that old id? Thanks for the help, Please?