Mistress

A mistress is a man's long-term female sexual partner and companion who is not married to him, especially used when the man is married to another woman.

The word mistress may also be used as a term for the lady of the house, especially one who is head of the household.

In the mirror universe, $𝜇$ was a Trill soldier of fortune who worked for the Terran Rebellion. She was the lover/mistress of $𝜇$. 

Gul Dukat, like many Cardassian officers during the Occupation of Bajor, conducted numerous affairs with Bajoran women, and had at least two mistresses, including Kira Meru, mother of Kira Nerys, and Tora Naprem, whom he claimed to love, and with whom he fathered a daughter, Tora Ziyal. 

Lady Sirella, daughter of Linkasa, was Martok's wife and Mistress of the House of Martok. Since as Mistress she has the duty of approving all marriages into the family, she came to Deep Space 9 to evaluate Dax's worthiness. Sirella later performed the wedding ceremony.