The Psychology Division was a branch of the United Federation of Planets Starfleet Medical.
In 2284, Doctor Krista Sivertsen was assigned to the Psych Division, where she treated Admiral James T. Kirk after he started having repeated vivid dreams related to the book Strangers from the Sky. (TOS novel: Strangers from the Sky)
In 2368, during a crisis leading to the destruction of numerous starships, a number of Starfleet Captains held eulogies over their destroyed vessels. Starfleet Medical's Psychology Division believed that this served as a form of closure and served as a way of sealing up a portion of the crew's life neatly and cleanly, thus allowing them to move on toward the next phase. (TNG novel: Grounded)