See Backing Up an Entire NIS+ Namespace. (Note that the old server you are replacing could be the master server for the domain, in which case you would run nisbackup on this old master server.)
Disconnect the old server from the network.
Connect the new server to the network.
Assign the new server the same IP address (number) as the old server.
Assign the new server the same machine name as the old server.
If necessary, stop the NIS+ service on the new server.
Run nisrestore on the new server to down load the NIS+ data.
Copy the .rootkey file from the backup directory to /etc on the new server.
Copy the NIS_COLD_START file from the backup directory to /var/nis on the new server.
Reboot the new server.