After the Four Kings and Queens left Narnia, the country was wracked by civil wars and petty squabbles (most notably the 17- year long war between the Red and Black Dwarfs) until at last the Council of Centaurs elected Crovian, a noble descendant of Lord Peridan, to the throne. His line, the now-forgotten Crovic Dynasty, lasted until the Telmarines conquered Narnia and killed every member of the royal family... and the fact that I just made all this up demonstrates that this portion of Narnian history is left pretty much up to our imaginations!
So that's okay, if the Netflix producers wish to expand the Dark Age of Narnia.
Perhaps it could all start with someone finding a lost scroll or tablet from the Dark Age...

Cleander

I think Lewis had a tendency to forget large chunks of history in Narnia in favor of telling a new story each time. LWW is very much a myth, even for Lewis, it seems. But at some point he must have gotten bored with Caspian’s time in PC, VDT & SC and wanted to revisit a more innocent time with HHB & MN. Then Lewis did LB, which puts a damper on much of what came before it.

He did yes, which is why I think it could leave the Dark Age open for interpretation

Lewis did outline a few things that happened in between LWW and PC in his timeline of Narnian history.

35 years after the Pevensies vanished from Narnia and 1050 years since the creation of Narnia, King Cor of Archenland was succeeded by the son he had with Aravis, Ram the Great. This was also mentioned at the end of HHB. According to the timeline Queen Swanwhite of Narnia lived c.1502... though this is contradicted by LB where Jewel says that Swanwhite lived before the reign of the White Witch. WikiNarnia speculates that there were two Swanwhites. In 1998 the Telmarines conquer Narnia and Caspian I becomes king. Telmarine rule continues in Narnia until the events of PC in 2303.

It's strange how little attention was given to that era in the timeline given how large it is (in comparison there are a lot more details given to the time between the events of MN and LWW).