# First I have to get the old IP address details and store it somewhere...
$OldIP = Get-NetIPAddress | Where IPAddress -like "192.168.*" | Where AddressFamily -like IPv4

# Then I have to delete it completely - It doesn't look like I can just change the values?
Remove-NetIPAddress -InterfaceIndex $OldIP.InterfaceIndex -AddressFamily $OldIP.AddressFamily;

# This is the bit where I thought it was a bit overkill. I can't create the new address until I completely remove the
# "NetRoute"/Gateway, whatever a netroute is, otherwise when I try and add it back in it says the Gateway already exists!
Remove-NetRoute -InterfaceIndex $OldIP.InterfaceIndex;

# And now I can finally add the new IP address in...
New-NetIpAddress -InterfaceIndex $OldIP.InterfaceIndex -IPAddress 192.168.0.123 -PrefixLength 24 -AddressFamily IPv4 -DefaultGateway 192.168.0.1