That was the Jeffrey Hunter as Captain Pike pilot episode, with Majel Barret as Number One, Leonard Nimoy as Spock, and John Hoyt as Dr. Phil Boyce.
The Pike character will be returning in May - Star Trek: Strange New Worlds. Supposedly ditching the universe that the current ST is in - the one with all the in-your-face PC, LGBT, whispering dialogue, nappy haired black super woman that saves the Galaxy form all threats.
My favorite star trek trivia question. What was the name of capris. Pikes horse? No google. See if you can remember.