A secretary was a person whose job was to perform tasks associated with the running of an establishment. This allowed those engaged in the primary function of the office, such as a detective, to better perform their job. Such functions would include meeting and announcing visitors, taking messages, and answering a telephone.
In the Dixon Hill holoprogram, the secretary of Hill's office was Madeline. Due to Hill's lack of work, however, she rarely received payment for her work. (TNG: "The Big Goodbye", "Manhunt", "Clues")
Constance Goodheart functioned as Captain Proton's personal secretary. (VOY: "Night", "Bride of Chaotica!")
In 1953, Darlene Kursky worked as Douglas Pabst's personal secretary. (DS9: "Far Beyond the Stars")
Roberta Lincoln was assigned as Gary Seven's secretary on Earth in 1968. (TOS: "Assignment: Earth")
In 2364, Trent was the personal secretary to Beata, the Elected One of Angel I. (TNG: "Angel One")
In 2371 a secretary worked in Brunt's office in the Tower of Commerce on Ferenginar. Quark paid him to see Brunt, to stand in the waiting room, to let Rom sit down, use the elevator, and lastly gave him something for his trouble when both men had to leave without seeing Brunt.(DS9: "Family Business")
In 2376, Nicole served as Admiral Owen Paris' personal secretary at Starfleet Communications. (VOY: "Pathfinder")
Quark once knew "the nephew of the cousin of the stepsister of a friend of the secretary to the consortium's chief accountant." It was through this connection he was able to learn that there was no drought on Balancar, which allowed him to acquire several cases of syrup of squill. (DS9: "The Magnificent Ferengi")