The prodigy graduated from Starfleet Academy in 2258. (Star Trek (App))
In 2259, Chekov was still serving aboard the Enterprise and had shadowed Montgomery Scott in engineering in order to learn more about engineering. When Scott abruptly resigned his position, Kirk made Chekov the chief engineer of the Enterprise.
Following his promotion, the warp core of the Enterprise was mysteriously disabled and Chekov was unable to explain what caused it. Later, during battle with the USS Vengeance, Chekov ran to the main deflector and flipped switches that allowed Scott (who had re-boarded the ship) to divert power from the ship's damaged warp core. Chekov also managed to save the lives of James Kirk and Montgomery Scott when the pair nearly fell to their deaths in the Enterprise's engine room during the ship's descent into Earth's atmosphere. (TOS movie: Star Trek Into Darkness)