Someone in here will know for sure and find this soon.
As far as I’m aware ship races are only officially done in arena commander. I’m not sure about needing to own a ship but I’d guess that you could rent a ship and components.
There’s plans to implement it in PU, Grim was recently updated to accommodate a viewing area, bar and every thing else to support betting and racing between the asteroids. I believe there’s some fluff on it so you could Google and do a bit of reading.
There’s a race called the Daymar rally that’s hosted in PU. It’s worth a Google and I think it’s run by the community. ADI had one recently that looked a lot of fun. It went across the lake on Microtech.
If you’re online and there’s others on mumble you can always say you want to do one. Everyone usually bundles onto a Carrack then descends upon some poor mining station. Everyone spawns a vehicle drives out into the middle.of nowhere then races back to the ship.
Just remember to set your respawn on the Carrack med bed