This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
The Carrington Award was one of the most prestigious honors granted by the Federation in the field of medicine, generally regarded as a lifetime achievement award. Five nominees were selected by the Federation Medical Council every year.
In 2371, the nominees were Doctor Wade, Healer Senva of the Vulcan Medical Institute, Doctor Henri Roget of the Central Hospital of Altair, Chirurgeon Ghee P'Trell of Andoria, and Doctor Julian Bashir of Deep Space 9. Bashir was the youngest person ever to be nominated for the award. Henri Roget was the winner of the Carrington that year.
In the Star Trek: Deep Space Nine Companion, Robert Hewitt Wolfe notes that the Carrington and the way that no one is sure which doctor was going to win is an in-joke to Star Trek: The Next Generation's Emmy Award nomination for its final season. It was believed NYPD Blue was going to win, but then it appeared that The Next Generation had a chance. In the end, neither won, as Picket Fences was awarded the Emmy.
In a line cut from "The Die is Cast", Vice Admiral Toddman noted to Julian Bashir that he was "in trouble", because the admiral had bet two cases of Saurian brandy that he was going to win the Carrington Award that year. Toddman told Bashir, "You lost, which means I lost. And I don't like to lose".
In the first draft script of "When It Rains...", Odo mentioned this award in a private conversation with Bashir. This was in response to the doctor explaining that he was trying to design a scanner that could detect if someone was being impersonated by a Founder. Interrupting him, Odo replied by rhetorically asking whether, if Bashir was successful in this attempt, he would "win the Carrington prize an unprecedented second time."