First Rani

You may be looking for Rani Chandra, a companion of Sarah Jane.

Ushas, known later as The Rani, was a renegade Time Lady. She knew the Doctor and the Master when all three were young and became an unwilling ally of the former and an enemy of the latter.

Youth and exile
The Rani was the same age as the Doctor. (DW: Time and the Rani) On the planet Gallifrey, at the Academy, she belonged to a clique of ten young people who called themselves the Deca. Both the First Doctor and her other future enemy Koschei belonged to this group. Her name at the time was Ushas. (PDA: Divided Loyalties)

At the Doctor's graduation, there was an incident involving the Rani and a giant rat. (DWM: Party Animals)

Unlike the other members of the Deca, she did not choose to leave Gallifrey but was exiled from the planet after some of her lab mice, as a result of an experiment, grew to enormous size and ate the President's pet cat. (DW: The Mark of the Rani)

Presence in Earth history
While the Rani certainly did not share the Doctor's fondness for Earth (she referred to it as a "miserable planet"), it was the focus of several of her research projects.

When the test subjects on Miasimia Goria, a planet she had enslaved, became violently restless and uncontrollable as a side effect of her experiments on them, the Rani visited Earth at various points in its history to extract chemicals from the brains of select human specimens. Because the chemicals in question enabled the human brain to sleep, and because the absence of these chemicals made her victims as violent and uncontrollable as those from her previous experiments, the Rani deliberately chose periods of social unrest to visit, using the violence to conceal her presence and its consequences. She visited the Trojan War, the Dark Ages, the American War of Independence, and finally the Luddite riots in the village of Killingworth during the early 19th century.

Prior to this arrival she had visited Earth in the late Cretaceous and acquired several Tyrannosaur embryos. (DW: The Mark of the Rani)


 * The Rani's comments concerning the unrealised full potential of the dinosaurs are curious given the existence of the Silurian civilisation on the planet at around the same time. She may have been obliquely alluding to averting the fall of the Silurians. Then again, as a biochemist she may simply not have been that familiar with social sciences such as history and just wasn't aware of the Silurians' existence. This seems unlikely, however, given her apparent visits to the Cretaceous to gather specimens.

The Master and, shortly after, the Sixth Doctor interrupted her work. The Doctor sabotaged the navigational system of the Rani's TARDIS, trapping the Master and the Rani inside as time spillage caused the Tyrannosaur embryos to grow at a dangerous rate. (DW: The Mark of the Rani).

On Terra Nova
Shortly afterwards, from the Doctor's subjective point of view, the Rani was also trapped along with the Sixth Doctor on Terra Nova, which the entity known as Iam had created. She had in the meantime tried and failed to manipulate the political situation existing between the three children of that reality's version of Cleopatra. (MA: State of Change)

On Tetrapyriarbus and Lakertya
On the planet Tetrapyriarbus, the Rani made the acquaintance of, and decided to employ, the Tetraps, led by Urak. With them, she invaded the peaceful planet Lakertya and put into motion a complex plan. The Rani abducted eleven scientific geniuses from across time and space, including Albert Einstein of Earth. Finally, she decided to "collect" the Doctor and attacked his TARDIS, causing the ship to go through turbulence and hit his head, triggering a regeneration into his Seventh Incarnation.


 * Conflicting accounts suggest that the Doctor did not regenerate strictly because of the Rani's attack on The Doctor's TARDIS.

The Rani channelled the intellects of the geniuses into a giant artificial brain which she believed could find the secret to manipulating strange matter, the key to making the planet of Lakertya into a Time Manipulator in order to correct what she considered to be errors in the universal timeline. Her first target was to be Earth, where she would prevent the extinction of the dinosaurs, creatures whose full potential she felt had never been truly realised. She considered the death of the native Lakertyans a small price to pay.

She used the artificial brain to find the answer as to how to create a lightweight substitute for strange matter, when it was devised she sent a missile containing the substance aimed at a strange matter asteroid. However, the Doctor destroyed the brain and redirected the missile. Urak betrayed her, leading the Tertraps against her, they placed her under house arrest (in her TARDIS) on Tetrapyriarbus. (DW: Time and the Rani).

After these events occurred, the Tertraps faced a food shortage crisis, while Urak managed to have the Rani put on trial, with the death sentence. She would have to solve the food shortage otherwise her sentence would commence. Two human and two alien prisoners were to be test subjects for the Rani's experiments in an attempt at solving the crisis. The Rani however teamed up with the four 'guinea pigs' and managed to escape the planet. Each then went their separate ways, with the Rani swearing to teach Urak a lesson and retrieve her TARDIS from him. (BBV: The Rani Reaps the Whirlwind)

Ultimate fate
Father Kreiner killed the Rani and the clone of the Master and kept their heads as trophies during the events of the Second War in Heaven. (EDA: Interference - Book One) However many aspects of the War took place in another timeline due to the Eighth Doctor's intervention, therefore leaving the ultimate fate of the Rani unknown. (EDA: The Ancestor Cell)

Personality
She was an evil (or, more likely, amoral) scientific genius whose villainy came not from the usual variety of lust for power and suchlike, but from a mindset that treated everything (including morality) as secondary to her research. She was known to enslave entire worlds in order to have a ready supply of experimental subjects and a place to carry out her experiments uninterrupted. Her major interest was in altering the biochemistry of other species.

While she did appear evil, she found the Master to be truly evil and therefore stupid. She simply did evil things because she felt it was necessary to her work. When the Sixth Doctor tried to convince her not to experiment on humans, she called them carnivores and asked if they ever thought of the lesser species when they sunk their teeth into pork chops. This shows that the Rani may have had a conscience of some kind, also shown when she was willing to destroy her test subjects because they would've killed the Doctor. (DW: The Mark of the Rani)

Behind the scenes

 * Kate O'Mara has, to date, portrayed the Rani in all of her television appearances as well as her single (to date) audio appearance.
 * It is not possible for the Rani to return in the revived series as the character's creators have not yet agreed to transfer their copyright of the character to any of the new producers.