I've gotten pretty far with earth rendering as in the attached picture. I'm looking into rendering stars. I really like how the stars are rendered in elite dangerous but I have no clue how to start working towards this. Has anyone worked on something similar that can give me some pointers on where to start?

www.shadertoy.com will have a lot about this. You can do a search on star...

By stars, what do you mean?

If you mean the star in the local star system. then you should look at things like this https://www.shadertoy.com/view/4dXGR4

If you mean background stars, that's a whole different subject.

Start with a nice sky dome and then think about adding some of the nearest stars as animated sprites.

For a good source try ESO.

https://www.eso.org/public/images/eso0932a/

This is a panoramic view of the Milky Way galaxy (use a sky sphere to render)

If you want to make your own, just look at how the real thing looks and make an image with random noise and use some filters to generate what you want.