2337

Events

William T. Riker's mother, Betty, dies. (TNG: "The Icarus Factor", "Interface")
Natasha Yar is born on Turkana IV. (TNG: "Legacy")
Trill Ambassador Odan negotiates a peace between the Alpha and Beta moons of Peliar Zel. (TNG: "The Host")
Beverly Howard dyes her hair brunette, but quickly changes it back. (TNG: "The Quality of Life")
The colony on Turkana IV begins falling apart, with dozens of factions fighting for control of Turkana City. (TNG: "Legacy")

According to the script for "Emissary", thirty-two years before that episode, i.e. in this year, a vessel of unknown origin, carrying a single lifeform of an unknown species, is encountered in the Denorios belt. This could refer to Odo, who was found in the Denorios Belt, though no date for this was ever given on-screen. The novelization of Emissary suggested this lifeform was a Changeling. However, the novel also specified that Odo was found in 2319.
The final script for DS9: "Rejoined" suggests Lenara Kahn was born during this year. [1]