Before removing/deleting the old one ensure the new one is set as the default email, just in case deletion of the old one doesn’t set the new as the default. It probably should do that but I don’t trust to probably.
I was also wondering how to change my email address because the current one is going to disappear soon. After finding nothing everything in my profile or the “Help” (not very helpful actually), I did a search in the forum and found a LOT of similar answers. Obviously, this function is requested a lot and quite often. Please consider making it more easily accessible to users.
On the other hand, in user profile page, please correct the bad English there for the word “Emails”. There, “emails” actually should have be written as email addresses.