Should we assume that the Zyxel device is now your "main" network router?
If yes, there are several problems with your plan
1) An AirPort Extreme has no audio support, so it would not work as an AirPlay device. Perhaps that you were thinking of an AirPort Express instead? The AirPort Express does have both analog and digital audio outputs, so it can function as an AirPlay device.
2) In order for the AirPort device to function as a separate router on the network, it must connect to the Zyxel router using a permanent, wired Ethernet cable connection. The AirPort cannot connect using only a wireless connection if you want it to act as another separate router.
If you do set up the AirPort as a second router, there is going to be a Double NAT error created on the network. This is not good, since Double NAT will often cause communication problems between devices on the network and also with connections from the Internet.
The recommended set up.....and the one that Apple will support......would have the AirPort device acting as a "bridge" to your Zyxel network....and not as a second router.
So, we need to 1) get clarification on which AirPort device that you have, and 2) how you want to set up the AirPort device.