Although the new series doesn't land on our screens until 2019, you may not have to wait much longer for more Game of Thrones after that.
According to HBO's Casey Bloys, the eventual prequels won't be ready to air "at least a year after the final season," which would make it 2020. As for details, Bloys was light but did say that the five proposed prequels are at different stages, but said that he doesn't want of them to detract from the final season.
"The final season has to air as the huge event in the TV season that it is. I don’t want to cheapen it with a spinoff airing right after it. That would diminish the achievement of how big and meaningful the show is," said Bloys.
The five proposed prequels come from some well-known writers, including Brian Helgeland (LA Confidential, Mystic River), Jane Goldman (X-Men: First Class, Kingsman), Carly Wray (Mad Men, Westworld, Mindhunter) Bryan Cogman (who's currently a producer on the show), and Max Borenstein (Godzilla, Kong: Skull Island).
On top of that, George RR Martin is working with two of the writers - Goldman and Wray - on their script as well. There's no definite timeline as to which gets the sign-off, however Bloys has indicated that it's "more likely one" that makes it through to air.