tvOS has no proxy field in its Wi-Fi settings, so the only way to route an Apple TV through a debugging proxy is a configuration profile — and Apple accepts a device-wide Global HTTP Proxy profile (the kind ProxyBeam generates) only on a supervised Apple TV. Supervision is a one-time setup you do once with Apple Configurator, a free Mac app. Two things to know before you start: it erases the Apple TV, and it works best on a model with a USB-C or Ethernet port.
Install Apple Configurator from the Mac App Store — it's Apple's own tool and it's free. There's no way to supervise a device without it.
Supervision has to happen before the device is set up, so start from a factory-fresh Apple TV. If it's already configured, erase it in Settings → System → Reset — otherwise Apple Configurator will prompt you to erase it later. Leave it on the Pair Your Remote screen. Nothing is stored locally on an Apple TV, so the reset just means signing back into your Apple Account afterward.
Connect the Apple TV and the Mac to the same router — Ethernet on the same subnet is the most reliable. Every Apple TV since 2017 dropped the USB port, so newer models pair with Apple Configurator over the network rather than by cable.
Open Apple Configurator and choose Apple Configurator → Paired Devices. Select the Apple TV, click Pair, and enter the six-digit PIN shown on the TV. On an older model with a USB-C port, connecting the cable pairs it automatically.
Select the Apple TV and click Prepare. Choose Manual Configuration and turn on Supervise devices and Allow devices to pair with other computers. Pick Do not enroll in MDM, assign an organization (this generates a supervision identity), choose which Setup Assistant panes to skip, then click Prepare.
Complete Setup Assistant on the Apple TV. Open Settings — under the device name you'll see a line noting the Apple TV is supervised. That's it: it now accepts a device-wide proxy profile, so you can install the one ProxyBeam generates.