The 18-year-old actress is set to star in an upcoming season nine episode of the BBC sci-fi series but with much of the cast big fans of Thrones, her casting posed an issue.
Lead actor Peter Capaldi "didn't want to know anything at all" about future plotlines from Williams, who plays Arya Stark in the TV adaptation of George RR Martin's A Song of Ice and Fire books.
Stars in Doctor Who and Game of Thrones
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Details of Williams' Doctor Who character are yet to emerge, but Clara actress Jenna Coleman said she was "utterly brilliant as you would expect".
"It's a very surprising and intriguing storyline with her connection to us and her connection to the Doctor," she continued, with Capaldi describing her performance as "cosmic".
"I love cosmic, it's such a great word, it covers so many bases," he said. "She's wonderful in it, and also, what's great about Maisie, she changes, she metamorphosises. She's metamorphic.
"She's so different, without giving anything away, the way she acts, the different aspects of her character, is very exciting and compelling and very impressive for someone who is so young."
The ninth series of Doctor Who is due to air on BBC1 this Autumn.
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