How do I delete and old email address associated with Apple ID on my computer?

Here's how you change the email address you use for your Apple ID:

1. Go to https://appleid.apple.com and sign in.

2. In the Sign-In and Security section, choose Apple ID.

3. Enter the email address that you want to use as your Apple ID.

4. Choose Change Apple ID.

5. If you changed your Apple ID to a third-party email address, check your email for a verification code, then enter the code. Learn what to do if you didn't get the email. --> If you didn't receive your verification or reset email - Apple Support

6. If you use services like iCloud or Messages to share with friends and colleagues, sign in to those services with your updated Apple ID. --> What to do after you change your Apple ID or password - Apple Support

For more details, read the document: "Change your Apple ID" --> Change your Apple ID - Apple Support

Try this:

Sign in to your Apple ID account page and edit / update your Apple ID details.

https://appleid.apple.com