House Velaryon doesn’t disappear in Game of Thrones ; it just loses most of its power and becomes easy to miss. In the books, they’re still around on Driftmark, but by the time of the main series they’re a much smaller, less influential house than they were during the Targaryen era.

What changed

The big turning point is the Dance of the Dragons, which badly weakens the house and its fleet. After that, the Velaryons never regain their old status, so by the time of Game of Thrones they’re basically a minor noble house rather than a major player.

During the main series

In the book timeline, House Velaryon is sworn to Dragonstone and sides with Stannis Baratheon during the War of the Five Kings. Lord Monford Velaryon dies at the Battle of Blackwater Bay, and his young son Monterys becomes the new lord. Their bastard kinsman Aurane Waters also becomes Master of Ships for a time before vanishing with the royal fleet.

Why they feel missing

The TV show trims a lot of the smaller political and naval storylines, so most Velaryon activity never gets screen time. That’s why they seem absent in Game of Thrones , even though in the wider lore the house still exists.

In one line

They survived, but as a diminished house: still alive in the lore, just no longer powerful enough to matter much in the main story.

TL;DR: the Velaryons were not wiped out in Game of Thrones ; they declined after major wars, stayed on Driftmark, backed Stannis in the books, and were mostly cut from the show.