Lost In Time

Lorilee Morgan. A household name among the officers of Starfleet in 2478. She was the youngest Captain in Starfleet history at the age of twenty, beating James Kirk by five years; she was one of three survivors of the Borg Collective; and she was the sister of Admiral Darren Morgan, the head of Starfleet.

James T Kirk. A household name among the officers of Starfleet in 2258. He was the youngest Captain in Starfleet history at the age of twenty five; a notorious womanizer; and he was the first and only person to beat the Kobayashi Maru (well he cheated but that doesn't really matter.)

When Lorilee is sent on a mission to the past she has strict rules that she needs to follow. No interfering with history, no betting on games in the past (Darren insisted on that one), and absolutely no interactions with James T Kirk. But that last one doesn't matter too much because what could two people two hundred and twenty years apart have in common?

A Star Trek Story. The Kelvin Timeline(ish)