Season 3 of House of the Dragon has done a lot of things already including getting Aemond Targaryen to Harrenhal in episode 2. We see Vhagar torch the garrison outside the castle, Aemond cut his way through what little resistance remains inside, and when he finds Ser Simon Strong and his sons eating dinner in the hall, he kills them. But one of those sons manages to get a knife into Aemond's back. Then Alys Rivers walks in and we have our "sick meet-cute," as actress Gayle Rankin put it.
By episode 3, the two of them have essentially vanished from the board. Daemon had turned Alys down when she had asked him for Harrenhal in episode 2, and now she has a wounded prince regent and the world's largest dragon sitting in the castle she wanted. We don't know yet what's happening inside those walls. But in the source material, there is indeed a romance between Aemond Targaryen and Alys Rivers.
MAJOR SPOILERS from Fire & Blood below.
What the Aemond-Alys story looks like in the book
In George R.R. Martin's Fire & Blood, this relationship is the version of the Harrenhal story that fans have been waiting to see on screen. The entire Daemon and Alys arc from season 2 with the visions and the potions was pretty much added by the show. In the source material, Alys and Daemon never share a single scene.
She belongs entirely to Aemond's story. When Aemond retakes Harrenhal in the book, he orders the execution of the remaining members of House Strong. He spares one person, who turns out to be Alys. He takes her as his companion and apparently becomes devoted to her.
He calls her "my Alys", and when Harrenhal is seized by Lady Sabitha Frey while Aemond is away burning the Riverlands, he returns and drives Sabitha out by fighting through whoever gets in his way specifically to get Alys back.
The last thing Aemond does before flying out over the Gods Eye to face Daemon, knowing it will likely kill him, as Alys's own visions seem to have foretold, is kiss her. He tells Daemon that it was Alys who knew where to find him and is said to have said it with pride. Then he gets on Vhagar and flies to his death.
Alys, for her part, is recorded to have watched from the towers of Harrenhal as Vhagar and Caraxes tore each other apart above the lake. According to Fire & Blood, she was pregnant at the time with Aemond's child.
The Alys mystery Martin never resolved
After the Dance ends, Alys surfaces again at Harrenhal, now ruling it with a band of outlaws at her back, claiming to be the widow of Prince Aemond Targaryen and the mother of his legitimate son. If she's telling the truth, that child has a genuine claim to the Iron Throne. They had apparently been married in secret before his death.
Martin never tells us whether she's telling the truth. Fire & Blood is written as history compiled by historians with their own agendas (a court fool, a septon, a Grand Maester) and none of them can fully account for Alys or verify her claims. It's one of the open questions the source text leaves behind and the show hasn't touched it yet.
We're only three episodes in but I think we will see more of Aemond and Alys in the coming weeks. House of the Dragon airs new episodes Sundays on HBO and HBO Max.
Add us as a preferred source on Google