This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
Psychiatry was a branch in the field of medicine that dealt with the diagnosis, treatment, and prevention of mental, behavioral, and emotional disorders. Psychiatry used a combination of psychology and drugs. One who practiced in this field was known as a psychiatrist.
According to Doctor Elizabeth Dehner's personnel file, she was originally posted to the Aldebaron colony for participation in tests and studies of other esper-oriented beings, which was the subject of a thesis that she was having published in association with the College of Medical Sciences of the Tri-Planetary Academy, during the early-2260s. (TOS: "Where No Man Has Gone Before" display graphic)
Dehner later transferred to the USS Enterprise from the Aldebaron colony, in 2265. She joined the life sciences department, assigned to the study of "crew reaction in emergency conditions." (TOS: "Where No Man Has Gone Before")
When Joe Tormolen (who was infected with polywater intoxication) attempted to commit suicide in 2266 and was later placed under restraint in sickbay, Captain James T. Kirk inquired if there was any information in Tormolen's record – namely, his psychiatric file or personality quotients – that might indicate why he was trying to kill himself. Commander Spock told Kirk that Tormolen probably wasn't attempting to do so, despite the fact that his capacity for self-doubt had always been rather high. (TOS: "The Naked Time")
After Jean-Luc Picard fell under the control of the Beta Renner cloud entity in 2364 and the senior staff of the USS Enterprise-D became suspicious of his behavior, First Officer William T. Riker had Dr. Beverly Crusher order medical and psychiatric exams on the captain, in order to back up their claim that he had lost his ability to command. (TNG: "Lonely Among Us")
In 2371, Quark illegally accessed Deep Space 9's personnel file on Kira Nerys, where he was able to download her voiceprint, retinal scan, and psychiatric profile, all in order to create a hologram of Kira for his client Tiron. (DS9: "Meridian")
In response to the absence of a ship's counselor on board the USS Voyager, The Doctor, who was not originally programmed with psychotherapeutic capabilities, developed a psychiatric subroutine in 2374 to add to his program. In doing so, he felt he would make himself "even more valuable" to the crew than he already was. (VOY: "Retrospect")
In 2375, Nog remained under constant psychiatric care for two months following the loss of his leg. After that time, it was revealed that his counseling sessions were going nowhere, because he was sick of talking about his feelings, and he began showing signs of depression: sleeping over eighteen hours a day and purposely missing his last two physical therapy appointments. (DS9: "It's Only a Paper Moon")
After ten days of incarceration in 2375, Tom Paris pleaded with The Doctor that he was "going crazy" and requested that The Doctor take him down to sickbay for a full psychiatric evaluation, followed by three or four days of observation. (VOY: "Thirty Days")
In 2377, Deanna Troi coerced Leosa into revealing who she worked for by suggesting that she herself would order the dabo girl to be held for extended psychiatric observation for the foreseeable future. (VOY: "Inside Man")