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Hecuba (also known as the Queen of Time) was a powerful being who ensnared sentient beings in games related to time manipulation, with their freedom as the stakes. She was the sister of the Celestial Toymaker.
The powers of Hecuba were similar to those of her brother, but while he was fond of games with toys, her games and traps were related to time and clocks. Her pocket universe was stabilised with her "Grand Chronometer" a giant timepiece capable of manipulating time and trapping the TARDIS in Time and Space. She was very beautiful, wearing the form of a glamorous actress of an earlier age in a luxurious ballgown. There is some indication that she could cast a glamour over her male opponents like a siren: the Second Doctor admitted she was beautiful even when she frightened him and Jamie was uncharacteristically complimentary to her beauty even though he knew she turned living people into clocks and she had stopped the Doctor's heart (Jamie was normally utterly protective of the Doctor and ready to attack anything that tried to harm him). Supporting this is Hecuba's antagonism to Zoe, whom she treated with impatience and disdain. The majority of her tests required Zoe to use all of her wits. At the same time, she was amused at Jamie and overlooked his intelligence, which gave him enough leeway to solve two of her games.
Her manner was flirtatious and coy, but she only cared about the amusement in her victims' fear and pain. She was vain, but the Doctor was sparing with his compliments, knowing she would never have enough. Hecuba was sadistic and enjoyed making the Doctor uncomfortable by encroaching in his space, teasing him, and forcing him to dance with her. (AUDIO: The Queen of Time)
Hecuba captured the Second Doctor, Zoe Heriot and Jamie McCrimmon, and made them play her games for her entertainment. Zoe and Jamie endured a series of tests (battles) with their lives at stake as she toyed with the Doctor over an elaborate and corrupted banquet of spoiling food. Her style of taunting the Doctor was much as the Celestial Toymaker forced Steven and Dodo to play his games as he played personally with the First Doctor.
Hecuba claimed to have "always admired" the Doctor's intelligence, and implied she had been told of him by another person, "You're one of a kind," and she didn't understand why the Doctor cared about his companions (just as the Celestial Toymaker didn't understand how the First Doctor could care about Steven and Dodo). One of her tests was to stop the Doctor's metabolism. Zoe had to find which of the thousands of clocks was bound to the Doctor's life in order to free him. They later learnt Hecuba's ultimate plan was to turn the Doctor into a Grandfather Clock.
The Doctor eventually escaped Hecuba's domain, trapping her in a time loop with her monstrous henchmen Snap and Dragon and Marie Antoinette for the rest of time. She swore revenge on the Doctor as her universe dissolved about her. (AUDIO: The Queen of Time)
Hecuba was bored, calculating, and cruel and found pleasure in "playing" with her victims. Her "favourite part" of the games was watching the Doctor's companions break down in defeat and she loved watching her phantom armies kill each other, though the graphic violence was real enough to sicken the Doctor. Her mood swings changed without warning, turning from snarlingly vicious to laughing at a second's notice. When Zoe first saw her, she couldn't tell if she were laughing or crying. The Doctor never dared drop his guard, knowing the slightest slip could be fatal, but he managed to prize small bits of information out of her by "playing" his own game of pretending to be completely ignorant and flustered.
All other visitors to Hecuba's domain had failed or refused to play her games. Hecuba turned them into clocks to keep for her eternal entertainment. She showed them her past clock-victims, clearly expecting him to be unnerved by the revelations. While she loved games, she preferred to win, and that meant cheat at every opportunity — much as her own brother the Celestial Toymaker did, only she was even more dishonest: she thought it was amusing to give Jamie false clues in the game to save the Doctor's life. Her style of cheating was different from his; she "stacked the deck" at every opportunity, giving Jamie and Zoe tasks that she believed would be out of their ability to solve. When they weren't amusing enough to her she grew angry at their lack of entertainment.
Hecuba expected the Doctor to amuse her, calling him a "worthy adversary," but she never calculated for his success. Any time the Doctor did something she did not expect, she reacted poorly. When he offered to "lay his cards on the table," she appeared particularly amused, for her brother, the Toymaker, loved to play cards.
Hecuba was vain. She looked like a "glamour" actress, appearing in a silver ball gown, bobbed blonde curls and blood-red nails and lipstick like a movie actress. She sought compliments. She was amused at Jamie's adoration and quick to be jealous of anything Zoe said or did. Because the Doctor failed to respond in predictable ways to her attempts at conversation, she wound up paying more attention to him in turn. (AUDIO: The Queen of Time)
The centre of Hecuba's game was a banquet. Each course was actually a hidden trap and the Doctor had to find some way of avoiding the meal but not show his disgust at the food itself. Hecuba had no problems with eating the disgusting fare, and ate with disturbing relish.
The first course was foul smelling oysters, in putrefaction. They were allegedly attached to Aphrodite, Goddess of Love. The Doctor deflected his portion of the banquet by saying, "Ladies First," and she countered by observing he was every bit as charming as she was "led to expect". When the Doctor claimed to not know her identity, she stopped his heart and ordered Jamie and Zoe to find the one clock in her collection of thousands attached to his life: if they did not, the Doctor would die in five minutes. Hecuba then announced, "I am Hecuba, Queen of Time. Let the games commence!" and laughed hysterically. As his companions fought for his life, Hecuba mock-mourned the helpless Doctor, admitting that the Universe would be dull without him, and how sad she would be when he died.
To Hecuba's displeasure, Zoe riddled out if the Doctor's heart had stopped, so had his clockwork. She thus found his clock and won the round.
The second course was celebratory cocktails.
Hecuba was not pleased Zoe had won, but when the Doctor woke up and recoiled from the oysters, she was genuinely pleased. She didn't want the game to end and preferred to deal with him as her adversary. She served cocktails of a very foul brew: Time Bomb. (AUDIO: The Queen of Time)
Behind the scenes
Because Hecuba is part of the Toymaker's family, she is definitely one of the Elder Gods, though whether or not she is a Guardian is unclear. Additionally, Divided Loyalties makes reference to Time Lord records which mention "a being or beings know as the Toymakers." If there are indeed more than one, and if she is family, Hecuba could be a Toymaker.