An antidote was a substance which could counteract a specific form of poisoning.
In 2151, a Klingon ship raided a Xarantine outpost and stole, among other things, Xarantine ale. The Xarantines, however, had bonded a carbon dioxide-based neurotoxin to a unique molecule of the ale. After the Klingons had consumed the ale, they became unsconscious and would have died within one or two days, but Doctor Phlox developed an antidote. (ENT: "Sleeping Dogs")
The Dramia II plague, which struck a colony on Dramia II in 2251, had no known antidote, but Saurian virus antibodies in the bloodstream of one of the original plague survivors created an immunity to the plague. (TAS: "Albatross")
In 2266, Doctor Leonard McCoy was forced to develop an antidote for the polywater intoxication. Almost one hundred years later, Beverly Crusher adapted McCoy's work to develop a new antidote for the stronger strain encountered by the USS Enterprise-D. (TOS: "The Naked Time"; TNG: "The Naked Now")
Commander Benjamin Sisko was skeptical about the orange bubbling liquid he was offered while in the third shap of the Wadi game Chula and thought that it could be a drug or poison, but ultimately it was the antidote for the gas. (DS9: "Move Along Home")
Makara herbs could act as an antidote to sedatives. While taking these herbs during her pregnancy, Major Kira Nerys was able to overpower Silaran Prin by pretending the sedatives he gave her worked. (DS9: "The Darkness and the Light")
The spread of the aphasia virus was halted through the efforts of Quark and Odo (who were both immune due their physiology), and Kira Nerys who forcibly brought Surmak Ren aboard the station in order to infect him and provide incentive for him to develop an antidote. (DS9: "Babel")
Chakotay and Janeway were infected with an incurable virus that necessitated them being left on a planet whose environment blocked the progression of the disease. Eventually, an antidote was found by way of an antiviral serum from Danara Pel for the disease and they returned to USS Voyager. (VOY: "Resolutions")