HTC One (M8) GPE is getting the taste of Android 5.1 and update is over-the-air. so you don’t need to follow some long process to get it. The update being just over 244MB large which packs all the new features and bugs fixes that comes with the 5.1 update.
Android 5.1 bring a better security for the device and the ability to control paired Bluetooth devices from Quick Settings, same goes for joining Wi-Fi networks. With all this it also provide HD voice support along with some improvements and animation. So if you are a owner of HTC One (M8) GPE (Google Play Edition) you can try the new firmware by checking for updates in the device Settings.