You want to move a name server to another address.
If you have three or more authoritative name servers registered with your registrar, remove the one you'll move well ahead of the change. This entails removing the NS record pointing to the name server in your zone data and using your registrar's interface to request that they remove the NS record delegating the zone to the name server from the parent zone. Wait until the NS record and corresponding A record are removed from your parent zone. After the move, change the name server's A record in your zone data and add the name server's NS record to your zone data. Then use your registrar's interface to request that an NS record delegating the zone to the name server at its new address be added to the parent zone.
If you only have two authoritative name servers, consider adding another and using the previous solution. If you can't do that, arrange to have the name server answer on both its old and new addresses for a period of time (for example, by adding an IP address alias on the name server's network interface). Then change the name server's A record in your zone and in your parent zone through your registrar. (You may do this through the same form that you use to register a name server, or at least a similar form.) Once you see the new record in your parent zone, wait until one TTL has passed. Then remove the old address from your name server's configuration.
The reason this is more complicated than moving a plain vanilla host is that a name server's address usually appears in two places: your own zone's data file and your parent zone. While you have direct control over your own zone, you must request changes to your parent zone through your registrar. And you can't be sure when the change to your parent zone will occur: it often takes a day or two for changes to take effect.
That's why removing the delegation to the name server that's moving ahead of time works well. It gives you the freedom to change the name server's address whenever you like. Then, after you've moved the name server, you can add it back at your leisure.
The reason this method doesn't work if you only have two name servers is that you never want to be left with only one authoritative name server for your zone. Consequently, you can't remove the delegation to a name server in advance of the move. You also shouldn't request the change of address through your registrar and try to synchronize the move with the change to your parent zone, since you'll inevitably end up with only one registered name server, at least for a little while.
6.7.4 See Also
Recipes Section 1.6 and Section 1.7 for information on the registration process, and Section 2.17 for the related process of changing data about a host that's not a name server.
BIND Name Server Configuration
BIND Name Server Operations
Delegation and Registration
Interoperability and Upgrading
Resolvers and Programming
Logging and Troubleshooting