AN ARYA-SIZED GAP IN THE PIRATE MARKET
It's also worth noting that pirates definitely hold a place in pop culture, and there is certainly space for a new pirate series. Pirates of the Caribbean was one of Disney's most popular film franchises, but seems to be foundering at this point in time. A reboot was planned and then canceled, and a sixth film was mentioned as a possibility in 2017, but there hasn't been a lot of movement on it since. Black Sails, the prequel series to Treasure Island, did reasonably well before being canceled after four seasons. With no current pirate series to compete against, and an existing fanbase that loves Arya and the Game of Thrones universe, a west of Westeros spinoff could be just what audiences want - especially as it would not only be a pirate series, but a true female-led one, something that is extremely rare.
THE PROBLEM WITH A PIRATE SPIN-OFF
Of course, no spinoff idea is perfect, and there are a few issues with this idea for where Game of Thrones can go next. For one thing, there is no clear villain or antagonist from the start - Game of Thrones struggled to wrap up their big villain arcs in the end, though, so perhaps a series without a big bad isn't the worst idea for a spinoff. A clear end for this series would be for Arya to travel all the way around the world and come home again... but then what? Another catch up on where Westeros is now, which would be logistically incredibly difficult to create.
Maisie Williams herself may also not be interested in spending several more years as Arya Stark. While she's clearly a fan of the character, a decade is often more than enough, and while her X-Men project is still set to release (although it's been pushed back to 2020), it's unlikely that this will become another big franchise role thanks to complications after Disney acquired the Fox rights. Like many other actors who became famous through a role at a young age, it's highly likely that Williams will want to expand her horizons and take on smaller projects to really show the range of her talents.
Finally, HBO programming president Casey Bloys categorically denied that this was a possibility (via THR) - even though the subject was brought up because there has been such buzz around it since the series finale. However, this doesn't necessarily mean that it couldn't still happen... or that, perhaps, the way to create an Arya spinoff without it is to create spinoffs for some of the other pirate queens mentioned above. Arya isn't the first woman to seek out what is west of Westeros, and an Elissa Farman show could be the perfect fit: fulfilling all the things fans want in an Arya series while remaining a prequel, expanding the lore, potentially connecting with another prequel spinoff set at the same time, and giving Williams the chance to appear at the start for a cameo, before the show goes further back in history to the women that came before this incredible female character.