Brienne is the sole surviving child and heir to Lord Selwyn Tarth. Lord Selwyn is the Lord of Evenfall Hall, which is the seat of House Tarth. The island of Tarth is located in the Stormlands. So, Brienne is of noble birth, but House Tarth is one of the minor houses of Westeros. Her claim would not be very good.
Gilly would have no claim. She is one of Craster’s daughters and a wildling.
Missandei is a foreigner and a former slave. She would have no claim.
Arya has the skills of the Faceless Men. She could pretend to be anyone (once they are dead and she takes their face). I could see her killing someone (Jaime Lannister?) so that she can get closer to Cercei.
It would be an epic twist if that happened and Arya was the last [faceless] “man” standing.
But I do worry that we have not seen the last of Jaqen H’ghar.
“Arya has the skills of the Faceless Men. She could pretend to be anyone...”
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I thought previously about how that could be an asset to Jon or Sansa, but you just made me remember how she was able to impersonate Walter Frey (that voice though) without detection. Who else could she be? Cercei would be a lot easier than Frey. Could we have someone like Cercei taking the throne, only in a final Shyamalan moment to find out it’s really Arya? That would be bittersweet.