The Stolen Earth
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The Shadow Architect was the leader of the Shadow Proclamation.
When The Tenth Doctor arrived at the Shadow Proclamation headquarters, the Shadow Architect dismissed the idea of him being a Time Lord. After he solved the mystery of the stolen planets, she asked him to lead the Shadow Proclamation into war with the Daleks, who had taken them from their places in time and space. The Doctor, pretending to comply, made an excuse to enter the TARDIS and escaped. (The Stolen Earth)
Later, the Shadow Architect oversaw the capture of the Doctor(Silver Scream) and put him on trial for interfering with time. Acting as judge, she found him guilty as charged. However, after The Doctor and his fellow prisoners saved her from corrupt Judoon and Krillitanes, she revealed the trial was false and he was free to leave. She warned The Doctor he would need his friends around him, “when he knocks the fourth time”. (Fugitive)
On orders from Davros, Colony Sarff visited her in their hunt for the Twelfth Doctor and tried to threaten her for information. She refused to tell Davros’ envoy where The Doctor was, and although she demanded to know what Davros wanted, Sarff told her nothing and left. (The Magician’s Apprentice)
The Shadow Architect was a humanoid with pale skin, white hair, and red eyes. She was the same species as a servant at the Shadow Proclamation. (The Stolen Earth)
BEHIND THE SCENES
Excluding River Song, actual historical figures, and distinct incarnations of existing Time Lords, the Shadow Architect is the only character introduced during Russell T Davies’ time as showrunner to later appear during the Steven Moffat era.