For reference:
Connect a PlayStation wireless game controller to your Apple device - Apple Support
Use Bluetooth accessories with your Apple TV - Apple Support
In general, set your game controller to Pairing Mode (press and hold the PS button and Share button until the light bar on the controller flashes), to make it discoverable for nearby host devices to which it hasn’t connected before.
Then, on Apple TV, go to the Bluetooth settings screen (Settings﹥Remotes and Devices﹥Bluetooth﹥), and find the controller mentioned there (probably under “ᴏᴛʜᴇʀ ᴅᴇᴠɪᴄᴇs”). Select it to connect and pair.
It should remember the pairing for future use (unless you reset the Apple TV, or pair too many other accessories), so that the pairing mode procedure won’t be needed the next time you want to connect this game controller to this Apple TV box.