Well, no problem. Fact is, if you have the HOS iPhone app, you can stream from the app to your Apple TV box using Apple's "AirPlay" wireless technology. And it's been that way for almost two years.
HOW COME I DIDN'T KNOW ABOUT THAT you ask??
Because Apple in its wisdom hides the icon that lets you know that AirPlay is ready to use. It's part of their "keep it simple" design policy, but this is one case where it really doesn't help.
The icon is only visible when you are  connected to a Wi-Fi network  your Apple TV (or other AirPlay device) is on the same WiFi network and  you are actually streaming something.
If all three of these conditions are met, you will see the AirPlay icon appear on the right hand side of the player control overlay that slides up from the bottom of your screen when you tap NOW PLAYING in the top status bar, or when you tap anywhere on a program playlist page. Here's what it looks like in action:
If you tap the AirPlay icon, you'll see a menu showing the name of your iPhone or iPad, plus your Apple TV, plus any other AirPlay devices like Airport Express or Airport Extreme hotspots on your WiFi network.
Choose Apple TV, and the AirPlay icon will turn blue to show you it's working. You can now stream HOS from your mobile device to your TV when the Apple TV input is selected. Sweet!
Any questions? Please email firstname.lastname@example.org.