You will need to go to the binding section of the new website (IIS Manager-> RightClick site-> Bindings) and select one of the IP addresses on the server. By default, IIS will receive one available IP address, so if you want it on one specific IP address, you will need to do this.
As long as this IP address can be scanned from the local network and port 80 is open on the network (which should be so), you do not need to do anything.
Muqeet Khan
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