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The pair were seen at Holywell Bay in Cornwall, shortly after it was confirmed that House Of The Dragon was officially in production.
It’s believed the show is being filmed at several beauty spots in Cornwall.
Watch: Game of Thrones actress Natalie Dormer is a new mum
The series is set 300 years before the events of Game Of Thrones and is inspired by the George R R Martin book Fire & Blood.
It is set to follow the story of the powerful Targaryen family and a civil war that took place known as the Dance of the Dragons.
Their descendant Daenerys Targaryen was a major character in the main series, with Emilia Clarke in the role.
The new series will star Paddy Considine as Viserys Targaryen, the king of Westeros.
Smith will play his younger brother Daemon Targaryen and D’Arcy will star as Rhaenyra Targaryen, Viserys' daughter by his first wife.
Other cast members include Steve Toussaint, Rhys Ifans and Olivia Cooke.
Earlier this week, bosses shared a picture of a socially distanced table read on Twitter, confirming that production was under way and that House Of The Dragon is due in 2022.
— House of the Dragon (@HouseofDragon) April 26, 2021
"Fire will reign. The @HBO original series #HouseoftheDragon is officially in production. Coming soon to @HBOMax in 2022," said the post.
Game Of Thrones came to an end in 2019 after eight series.
The show was a huge hit and scooped a raft of accolades, including more than 50 Emmys.
Watch: 'Game of Thrones' Prequel 'House of Dragons' Begins Production