Lieutenant Ballard was a Starfleet officer in the sciences division assigned to the USS Enterprise-D in the 2360s.
In 2366, Lt. Ballard was teaching classes in the ship's school when Lieutenant Commander Data attempted to enroll Lal in primary school classes. She had conferenced with Data regarding the difficulty of having a young android interact with humanoid children. (TNG: "The Offspring")
Lt. Ballard was played by Judyann Elder.
While she might have been an officer assigned to take charge of the ship's school, its also possible she also had another position in the science or medical departments.
She is the highest ranking Starfleet officer shown teaching or supervising in the ship's schools and nurseries.