Can you connect an external hard drive to an Apple TV?

Certainly. While an Apple TV doesn't natively support connecting an external hard drive for the purposes of accessing personal media directly, there are workarounds which involve using other devices and apps. For instance, one can connect an external hard drive to a computer or a network-attached storage device (NAS), and then use media server software like Plex or Infuse to stream content to the Apple TV. The Apple TV itself houses only internal storage intended for apps and cache, with no direct means to expand storage via external hard drives or USB media. Hence, direct connection and access to external storage isn't provided out of the box, but with the right setup on your home network, accessing content stored on an external hard drive is absolutely feasible.