Im currently developing a site which will replace an old one located on a different webserver.

Ive logged into to change the nameservers from the old site to the new one, but it has not changed yet (although I am aware it may take some time)

In the old sites cpanel, underneath "advanced DNS editor", its showing alot of stuff:

If I have changed the Nameservers over, do I have to do anything with these? Do I have to copy them onto my new host's cpanel (with different IP address which is
The email settings are not important as I can re-create new emails on the new site.