When migrating or upgrading servers you can be faced with a situation where you have to shut down the live server, and bring up the replacement one.
If they are on the same VLAN (which makes sense), this sudden change can cause more downtime that it should, because the switch still has old mappings for the IPv4 and IPv6 addresses. On a Cisco switch, you should manually flush both the IPv4 ARP and the IPv6 neighbor entries:
gatekeeper#clear arp-cache 192.87.30.4 gatekeeper#clear ipv6 neighbors vlan 2 2001:610:148:dead::3
If you do this right after the old machine has shut down, then the new one will be reachable right away.