How can I use icloud after changing apple ID

I changed my AppleID. In the Icloud on my mcbook is still the old no more existing mailadress deposited. The Icloud wants me to enter the password of the old Mailadress, which is the same as the password of the new mailadress.

How can I change the Mailadress in the Icloud to the Mailadress from my AppleID?