Q: Deleting unused Apple ID from iPhone?

A while back, I used an old email address for my Apple ID, which I have since changed. On my current iPhone I have set it up since purchasing, with this new apple ID which thus corresponds to my new email address.

I am trying to delete/remove the old Apple ID from my old iPhone, as I wish to erase everything on it, to give to somebody else to use. The problem is that I don't remember its password, and I don't even use that email address anymore (the email account may even be closed; even the apple ID may be closed?!) and so I don't have access to the email address either. This means I am unable to access any links sent to the email, to reset my password.
Frustratingly, the security question answers I am inputting are also not giving me any luck.

So my question is: how can I delete this Apple ID from my phone? Is there a way to erase everything/reset my phone without apple ID? Or perhaps, is there a way to send the reset link to my new email address?