You want to change all of the registered name servers for your zone.
If you can, arrange to have the old name servers running and authoritative for your zone throughout the change. This still makes the process easier.
First, configure the new name servers as authoritative for your zone (or, if they're run by someone else, like your ISP, ask that they set them up). Once the new name servers are configured and answering authoritatively to queries in your zone, add NS records to your zone data for the new name servers and request that your registrar add those name servers to your zone's delegation information. When the delegation information has been updated in your parent zone, request that your registrar remove the delegation to the old name servers. Once that delegation information is gone from your parent zone, wait for one TTL on the delegation records to pass, then remove the NS records for the old name servers from the zone and, if you want, decommission the old name servers.
Arranging to have both sets (old and new) of your name servers running simultaneously helps you make the required changes on your own schedule. It would be nearly impossible to coordinate the simultaneous decommissioning of the old name servers and commissioning of the new name servers with the changes to your zone's delegation information in your parent zone. With both sets running at once, you can ask your registrar to add the new ones, wait for the new delegation information to appear, then ask the registrar to delete the old ones.
When you establish the new authoritative name servers, you may initially want to configure them as slaves for your zone, loading from the primary master. If the primary master is among the name servers being decommissioned, you can later move the primary to one of the new name servers and reconfigure the other slaves to transfer from the new primary.
6.8.4 See Also
Recipes Section 1.6 and Section 1.7 for information on the registration process, and Section 6.7 for instructions on moving just one name server.
BIND Name Server Configuration
BIND Name Server Operations
Delegation and Registration
Interoperability and Upgrading
Resolvers and Programming
Logging and Troubleshooting