AO3 is where all the deep cuts live, and that's definitely true for the 'House of the Dragon' crowd. I sort by kudos or bookmarks, filter for the 'Reader' character tag, and then usually add 'Series' to the search. What works for me is finding an author I like—someone who nails a specific character's voice, like Daemon's chaotic energy or Rhaenyra's stubbornness—and then checking if they've written a connected sequence. The site's subscription feature is a lifesaver; you can follow a series and get emails for new installments, which beats checking back manually.
Some of the most popular ongoing ones seem to be Aemond-centric, no surprise there. There's a tension in those stories that writers really latch onto. I'd also peek at the collections on AO3; sometimes users curate lists like 'HOTD Series Masterlist' or 'Longform Rhaenyra x Reader,' which can shortcut the discovery process. Tumblr still has a pulse for this too, with writers linking their AO3 series from their blogs, often with moodboard aesthetics that set the tone before you even click.