"It's always a little apprehensive when you turn your baby over to foster parents," Martin said.
"But I'm involved in this. It's great to have Ryan, who's a great writer and someone who really knew my work. He's going to do his best to remain faithful to it.
"There's always a little suspense too … How good is it going to be? But I think I'm in good hands with Ryan and Miguel."
At the height of Thrones outcry, when millions of fans signed a petition for the eighth season to be rewritten, Martin issued a scathing statement hitting out HBO producers for compromising his work.
"It can be … traumatic," he told Fast Company in 2019. "Because sometimes their creative vision and your creative vision don't match, and you get the famous creative differences thing — that leads to a lot of conflict.
"The [final] series has been … not completely faithful. Otherwise, it would have to run another five seasons."
In A New Reign, which also gives fans a sneak peek at behind-the-scenes footage, Condal said Martin's narrative played a "huge influence" when he began writing the screenplay for House of the Dragon, as he acknowledged the pressure of surpassing viewer expectation.
"It's an incredible feeling to achieve my dream job. You get that great call which is the thing every writer is hoping for, and you're happy for a few seconds, and then you realise the responsibility that's on your shoulders," Condal said.
He said production on the prequel featured "the biggest sets I've ever been on, the biggest locations I've ever been on, the biggest crews I've ever seen. It's staggering."
Elsewhere, Sapochnik, who directed some of Thrones' most memorable episodes including season six's Emmy-winning Battle of the Bastards, admitted it was almost "too much of a challenge" to return to the world of Westeros.
But, he conceded, "You have to start by respecting it. You can't start by doing different for different's sake."
He added: "[It's about] realising what worked in Thrones and what didn't … What do we want to better? How do we want to evolve?".