This article explains how to make a missing AirPlay icon appear again.

AirPlay is built into iOS, so you don’t need to install anything to use it, and it can’t be uninstalled. It can, however, be turned on and off.

To fix a missing AirPlay icon, follow these steps:

Turn on Wi-Fi. AirPlay only works over Wi-Fi, not mobile networks, so you must be connected to Wi-Fi. To turn on Wi-Fi on your iOS device, go to Settings > Wi-Fi and tap the switch so it turns green.