Is there any way I can create a new email/outlook account and connect my old Xbox account...

the account connected to my old gamertag is a microsoft account, but it doesn't have @outlook or @hotmail) and the new email account that I want to be connected to my old gamertag is also a microsoft account but @gmail, not @outlook or @hotmail

Basically you can change the email associated with that old account but would not be able to use your current outlook account to do it you can either create a new outlook account or use another non MS server email account (google, yahoo, ISP) that is not
already a MS account and add it to the old account and then make that email the primary alias and remove your dads old email from the account.

Hi Eric! I'm Rostom, an Independent Advisor. I will be glad to help you here.

Please be informed that it's not possible to add a new Outlook email address that's already existing to another Microsoft/Xbox account. The Outlook email address you have is technically a Microsoft account. There's no way we can merge Microsoft accounts.

If you want to replace the email of your current Xbox profile, simply go to https://account.microsoft.com/ > Your info > Edit account info. There will be an option to create a new Outlook email address there. You can only add an existing email address if it's a 3rd party email address that is not currently linked to any Microsoft accounts.

Since it is an outlook account which is already a MS account you will not be able to use that email for your old account.

You would either need to use another Non MS server email like gmail, yahoo, or something like that or sign into your old account at account.live.com/addassocid and create a new outlook account to add to that old account.

The only thing you can do is set up a new email for your son.

OR

If this is a outlook email, it will be associated now with an xbox account and you would have to move that to another email.

Best solution create a new account and then move your alias to that. There is not way to merge accounts.