It's likely we'll never see Star Wars: Battlefront III. The game has been in development limbo ever since Free Radical Games was shut down many moons ago. Every once and a while we hear whispers in the wind that development is still ongoing for the much-desired third entry in the series, but we're yet to receive a confirmation one way or the way from LucasArts or whichever development team is currently attached to the project (rumors point to Pandemic and/or Rebellion in recent years).
That's why the below YouTube video makes us all the more sad. User Borman18 has uploaded some pre-alpha footage of Star Wars: Battlefront III. The footage is rough, understandably, but it gives us a good indication of what Free Radial Games was doing with the Battlefront series before the studio was shuttered. Specifically, their awesome planet-to-space technology, which made transitioning from fighting on the ground to shooting Star Destroyers in orbit a seamless process. The video also shows off some of the missions from the game's single player campaign.
The real bummer here is that we'll probably never be able to play this baby with our own two hands. According to Free Radical, the tech powering their version of Battlefront III died with the studio. If Battlefront III ever sees the light of day, it's probably going to look nothing like this. So for now just enjoy the footage and wish upon a star for Battlefront III to see release some day, in one form or the other.