you can use home sharing, you won't be able to share directly from the drive, you'll need to
import it to the appleTV app on your Mac, and then
enable sharing. This can be a bit clunky when using your own files.
or you can use infuse, which allows you to access network shares directly, you can either share files from the drive using a computer, or use a NAS device instead of the external drive. You just need to share it using SMB (or windows file sharing). Infuse will also tag your media, so you can select a movie name, instead of a file name. The tagging happens directly in the infuse app on the appleTV. This requires very little processor power on the device serving the files.
or you can use plex (
full description here), which runs a server program on your computer (or some NAS devices), it will set up your own streaming service (similar to Netflix or any of the other apps), it also tags all your media, you can then access from anywhere in the world, as long as the connection speed on both ends (your house, and wherever you are) can handle it. If you player is on the same network as your server, then your outside connection speed doesn't matter. You can also have your friends set up their own accounts and then share your media with them if you want.
they have apps for aTV, iOS, android, and a lot of smart TVs. You can also watch your content in a web browser.
If the player device you're using won't handle a file in its current format, Plex will convert it on the fly to a format that will work. You will need a decent powered computer for that. You can also have it pre-convert files if your computer isn't fast enough to convert as you watch.
Plex also has a decent sized free (but ad supported) library that you can access in addition to your own files. The ads only apply when watching Plex's content. Your personal content will not have them. You can also hide and ignore their content if you want.
Plex is free to use, they do have an optional paid level that gives you additional features, like being able to sync media to your phone.
for either infuse or plex, you will need a computer on and running when you want to watch the files, in most cases even a Raspberry Pi has enough processor power to handle streaming to either app, and will use much less power than leaving a full computer on 24/7. The Pi probably won't handle converting files as you watch though.