mail.domain.com instead of domain.com/webmail

Hello-
I have a domain that has been setup and running for years. The client has created a new web site and wants to host it elsewhere, keeping their email with me.

I used to have a sysadmin who handled this for me, but no longer do and he’s busy and tough to get a hold of, so I’m learning on the fly.

What I need to do:

I maintain DNS on their behalf so I have control over that.
I’m just a bit paranoid about breaking their stuff.

Any guidance would be appreciated. Previous searches have sent me down many rabbit holes and confused me more.