Changing DNS host records

Hello It has been over a decade since I’ve done this and need some help refreshing my memory. I have many customers that have registered their domains against my authoritative servers (DNS-AUTH3.CROCKER.COM). I need to move that machine to a different network/IP address. I’ve made the updates in my domain (crocker.com) but I think I also need to update the host glue records in the gtld-servers as well. How do I go about doing that? Ultimately the customers need to update their registration with our new authoritative servers, many have but we still have some stragglers I don’t want to break when I shutdown the old servers. Thanks -Matt