You don't give a lot of detail but I'm assuming you mean that you have a server\service at 184.108.40.206 that used to be at 220.127.116.11, right? If so, are both ip addresses allocated to your organization and do they both get routed to your network? If yes, then I think you could probably use NAT at your router/firewall to translate anything coming in for the old address to the new address.
Also, if the server\service is for web hosting, email, ftp, etc., etc. why not just change the DNS records for those resources to point to the new address?
Can you elaborate on your question?