Yes, there are unofficial radio stations which you can find at:
https://inara.cz
Radio Sidewinder and Hutton Orbital Radio are the best IMO. Radio Sidewinder plays weird kinda electronic/techno stuff which fits into the game well and you could imagine people listening to in the 34th century. Hutton Orbital plays an eclectic mixture of rock, pop and other genres (including the occasion Disney song). Both have GTA style adverts occasionally set in the Elite universe, as well as news updates and Hutton Orbital has a weekly podcast.
Third Rock Radio is affiliated to/run by NASA, so obviously doesn't have the Elite element to it.
So just pick the ones you like the sound of and run it in the background as you're playing. It does make it seem more real tbh.
Sorry if this sounded like an advert.