Steven Conrad is best-known for writing the films The Weather Man, The Pursuit of Happyness, The Secret Life of Walter Mitty and Wonder, as well as creating the TV series Patriot, Perpetual Grace, LTD and Ultra City Smiths. Conrad (under his Elephant Pictures production company banner) would work on the prospective series as writer, executive producer and presumably showrunner.
The Tales of Dunk & Egg is based on the Dunk & Egg series of novellas by George R.R. Martin. So far three have been published: The Hedge Knight (1998), The Sworn Sword (2002) and The Mystery Knight (2010), previously assembled and published as A Knight of the Seven Kingdoms (2015). Martin has a fourth novella partially written, The She-Wolves of Winterfell (working title), and between nine and twelve stories planned in total.
Martin previously proposed a Dunk & Egg series to HBO, before changing his mind on the idea due to the novellas being incomplete and not wanting to be overtaken by HBO again, as happened with Game of Thrones itself. However, with work on the main Song of Ice and Fire series still incomplete, it appears that Martin has changed his mind again and may see a TV series as a way of expanding and completing the Dunk & Egg series in a shorter timeframe.
The Dunk & Egg stories, which begin ninety years before the start of A Song of Ice and Fire (and Game of Thrones), revolve around the misadventures of Ser Duncan the Tall, a lowly hedge knight who acquires a squire named Egg, who is more than he seems. Dunk and Egg travel the Seven Kingdoms and become embroiled in various scrapes, some low-key stories and other adventures with more important ramifications for the history of Westeros.
The project remains in the development phase and has not so far been greenlit by HBO. Another spin-off series, House of the Dragon, has almost completed shooting of its first season for a project Spring or Summer 2022 debut on HBO. HBO is developing several additional prequel and spin-off series but has so far not greenlit any more.