Why would you need to ADD a new Client. Unless the APE sytem is completely different then any other Wireless router the printer should get an IP address from the router. That is IF the printer is setup to get an IP from the LAN DHCP server.
Now you may want to make that IP it does get a Staticly assign IP address so it never changes, which will screw up printing if it does change. But i don't know if you can do that with APE routers.
I'm trying to add my HP wireless printer as a "new client" to my wireless network using Airport Utility, but I can't find that option in the new version. I've downloaded all available updates of the OS and the utility.. Help!
You connect your HP using the HP printer controls, not Airport Utility.