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House Of The Dragon season 2 introduces two new characters, Addam and Alyn of Hull, who claim that Corlys Velaryon "owes" them. While the show hasn't explicitly said it, the implication is that Corlys Velaryon is their father, and they've kept his secret for years.
Corlys Velaryon has a reputation as an explorer and great naval leader, and fathering bastards would be damaging to his reputation. Corlys, however, feels guilty about how Addam And Alyn were raised, especially now that his own children are gone and he has no heir to Driftmark. He feels indebted to them, especially since Alyn saved his life in the Stepstones.
Addam and Alyn are introduced in "Fire & Blood" as Dragonseeds, bastards of Valyrian descent who are brought forth to try and claim dragons. Their mother claims they are Ser Laenor Velaryon's sons, but this is clearly not true, especially given their ages in the show. Corlys Velaryon is complicit in keeping this a secret. It is revealed in "Fire & Blood" that Princess Rhaenys, Corlys' wife, would not have been happy to discover her husband fathering bastards, especially with a shipwright's daughter.
Rhaenys is not characterized by a hot temper in the show, but it is understandable that she would react this way. Addam and Alyn are beneficial to Corlys because they are his bloodline and could be legitimized to carry his name and legacy forward. This is important to Corlys, who is passionate about legacy and history.
Addam and Alyn are Dragonseeds, like Hugh and Ulf, who will vie for an opportunity to claim dragons and fight for the Blacks. Corlys brings Addam and Alyn forward to participate, giving them opportunities to prove themselves. Addam is able to claim the dragon Seasmoke, which was previously ridden by Laenor Velaryon, Corlys' late trueborn son with Rhaenys.
Corlys eventually legitimizes both Addam and Alyn as Velaryons, making Alyn his rightful heir. While Alyn fails to mount a dragon, he eventually becomes the Lord of the Tides after the Seasnake's death and has his own Great Voyages, much like his father. Addam and Alyn are important characters to watch in the future of House of the Dragon.