Mistress

Mistress was the female equivalent of the title Master. After regenerating into female form, the Master took the name, short for Mistress. (TV: Dark Water)

Titus Craven offered Flip Ramon the opportunity to become mistress of a plantation in Jamaica. (AUDIO: The Behemoth)

The K9 robots commonly addressed their female associates as Mistress. Leela, companion of the Fourth Doctor was Mistress to K9 Mark I. (TV: The Invisible Enemy etc.) Likewise, the first two incarnations of Romana were referred to as Mistress by K9 Mark II. (TV: The Ribos Operation, TV: The Creature from the Pit etc.) Sarah Jane Smith was the Mistress of K9 Mark III, who had been left to her by the Doctor, (TV: A Girl's Best Friend) and K9 Mark IV, who was left to her by the Tenth Doctor following the destruction of K9 Mark III. (TV: School Reunion) In addition, K9 Mark IV addressed Rani Chandra as "Mistress Rani". (TV: The Wedding of Sarah Jane Smith etc.)

Chip, a force grown clone, addressed the Lady Cassandra O'Brien.Δ17 as Mistress. (TV: New Earth)

Urak, leader of the Rani's Tetrap servants, addressed her as "Mistress Rani". (TV: Time and the Rani)

As a lover
In the 18th century, Madame de Chateauroux was the mistress of King Louis XV of France until she became ill to the point of death. Following this, Jeanne-Antoinette Poisson, or Madame de Pompadour, became the King's new mistress. As the Tenth Doctor explained to Rose Tyler, Louis already had a queen, to which Rose responded, "Oh, I get it. Camilla," which Mickey Smith found amusing. Mickey was surprised to learn that "the King's wife and the King's girlfriend" got on very well, with the Doctor observing that France was a "different planet" to the 21st century Brits. (TV: The Girl in the Fireplace)

Oliver Charles had a mistress, who was "enjoyed" by a member of the Slitheen family who had secretly killed him and used his skin as a disguise. (TV: Aliens of London)

As an adjective
K9 Mark 2 noted that the all-female Ukkan librarians had completely mastered, or rather "mistressed", the art of archiving. (TV: Lost Library of Ukko)