Setup an extended Wi-Fi network using a spare Apple Extreme Base Station.

I recently changed my main router from an AEBS to another TPLINK router. Therefore, my main Wi-Fi station is not Apple. However, the signal on a part the house is rather weak, and having a spare AEBS, I tried to set it up as a repeater to extend the network. I do not intend to use an ethernet cable to connect both stations.

However, I ran into trouble while setting it up, since the AirPort application doesn't even recognize the AEBS, only when it's cable connected to the router. And when it does connect, it doesn't offer an option to create an extended network.

Is setting up a connection like this even possible?

Thanks to all of you for your time.