will an apple tv a1427 support local streeming

That would be a 3rd gen, which does not run apps. You would need a 4th gen or 4K model in order to access the app store and download any content, you would then need to look into live streaming services or connect an antenna to the network (using hd home run) and run the channels app to view that content on Apple TV.

If the local streaming has an app or you can erect an antennae and receive live content.

https://www.imore.com/how-watch-live-tv-your-apple-tv-without-cable