The assistant chief engineer or assistant engineer was the primary assistant or backup to the chief engineer.
In situations when the chief engineer is away from the engine room, the assistant chief engineer is responsible for overseeing engineering until the chief engineer returns. (TNG: "The Naked Now")
If a chief engineer is either incapacitated or killed in action, the assistant chief engineer is made chief engineer. (VOY: "Caretaker", "Parallax")
List of assistant chief engineers
Varro generational ship
Unnamed Y-500 class freighter