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