Just to be sure if I understand your objective correctly, you do mean that any visitor/user who try to access Plesk on the URL of your previous server gets redirected to the URL of Plesk on your new server?
If that's the case, and you've used a (sub) domain you own as the servers hostname, you could add that (sub) domain as a domain to your current server. Create a .htaccess file to redirect visitors from that domain to the host name your new server. After which you'll need to point the corresponding DNS records of domain to your new server.
(And perhaps configure a new hostname on your old server if you still need Plesk access to that server. Which can also be done via the IP off course).