Change alternate email in Edit Security settings

I am trying to change the Email in my "Edit Security Setting," because the email listed there has been closed a long time ago.

I keep getting

"Help us protect your account

Since you're trying to access sensitive info, we just want to make sure this is you. To continue, check your email and enter the code we just sent you."

There doesn't appear to be any way to delete that email. As I said, that email account was closed a long time ago and I wanted to input another (new) email account where my security code could be sent.

How do I input another email (new) account?