A first mate is the second-highest ranking officer aboard a civilian starship, the equivalent of a military organization's first officer.
In 2268, Kreel was the first mate of the Windjammer under Captain Black Jack Nova. (TOS comic: "The Flight of the Buccaneer")
In the 2270s, Jack Corrigan was the first mate of the Werewolf under Captain Solomon Kane. (FASA RPG module: Orion Ruse)
In the 2370s, Wayne Sheppard was the first mate of the SS Xhosa under Kasidy Yates. (DS9 novelization: The Way of the Warrior)