- You may be looking for the screen-headed servants of the Kings of Space.
Sphinxes were a species or class of beings with leonine characteristics. Although, prior to the rationalisation of the universe, they had been living creatures of magic, most sphinxes in the Time Lords' world were merely stone statues. Living sphinxes had a propensity to pose riddles.
History
In the mists of Gallifreyan history, the Pythia went to the island of Thule to steal the eye of its resident sphinx so that she could put it in place of her own eye that she had gouged out. (PROSE: Cat's Cradle: Time's Crucible)
However, as beings of magic, sphinxes disappeared from such planets as Earth when they began relying on technology instead, (AUDIO: A Spoonful of Mayhem) irrationality and sorcery having been beaten out of the universe by Rassilon and other early Time Lord reformers, (PROSE: Cat's Cradle: Time's Crucible) such as Urizen, through the Anchoring of the Thread. (PROSE: The Book of the War)
As evidenced by the fame of the Martian Sphinx (PROSE: Impractical) and of the Atlantean- (AUDIO: The Eye of the Scorpion) or Osiran-built Great Sphinx of Giza, (PROSE: The Sands of Time) sphinxes were, in the universe of rationality, relegated to nonsentient stone likenesses and legends, found in different variations in Greek and Egyptian records. (PROSE: EarthWorld)
However, as was known to Missy, at least one seemingly-inert sphinx statue in London still had a spark of life to it; through a complex blood ritual, she successfully awoke it for a time and interacted with it in the late 19th century. (AUDIO: A Spoonful of Mayhem)
A "huge" simulacrum sphinx with wings like an eagle's was housed in the New Jupiter EarthWorld theme park's Egyptian Zone, although it was criticised for mixing and matching features of the Greek and Egyptian lore on which it based itself: the riddle of the sphinx, "What walks on four legs in the morning, two legs in the afternoon, and three legs by nightfall?", to which the answer was "man", was one of the elements it took from the Greek accounts; on the flipside, it had a missing nose like the Great Sphinx of Giza statue. As a tourist attraction, the artificial sphinx would ask the riddle of park guests; during her particularly hectic adventures in the park, Anji Kapoor gave the answer before it was asked because she was trying to outrun robotic dinosaurs. (PROSE: EarthWorld)
As witnessed by the Tenth Doctor and Donna Noble, Jason and the Argonauts also encountered a sphinx-like being from the planet Satroz when an alien prison ship crashed on Earth. She was shot dead by the Parthenope prisoners. (PROSE: Island of the Sirens)