Reflector Director uses mDNS technology to discover your computer running Reflector 4. If you are unable to see Reflector 4 from the Reflector Director app, this is most likely because your iPhone or iPad is not on the same network or subnet as the computer running Reflector 4. It's also possible that mDNS traffic is not allowed on your network.
Ensure both of your devices are on the same network and try relaunching Reflector 4 and Reflector Director.
If mDNS or network limitations prevent pairing, you can also use a Quick Connect Code to pair Reflector Teacher to Reflector Director.