Q: I have an old apple ID that has my e-mail associated with it how do I remove the old ID?

You should jus update your o”old” AppleID with new info and continue to use it.

Where do you want to remove it from?

Everything, including all purchased apps, are associated with your old Apple ID. Just because you change your email address doesn't mean you have to abandon your old Apple ID. If you do decide to abandon your Apple ID and create a new one you will have to purchase again any apps previously purchased with the old ID.