A Design Engineer was a senior manager with extensive experience in and knowledge of starship engineering. He or she were tasked with supervising teams of engineers, were intimately familiar with the design of the ships under construction, and were responsible for implementing changes to these ships.
In her career summary, after working as Design Team 7 team leader, Doctor Leah Brahms became a Design Engineer for the Theoretical Propulsion Group. When working at the Utopia Planitia Fleet Yards, she supervised the implementation of improved subspace field generators on the Galaxy-class starships USS Enterprise-D and USS Yamato. She was, then, named as a Starfleet Design Consultant. This information, which was current for 2366, was from her biographical data file. (TNG: "Booby Trap", okudagram) A year later, in 2367, Dr. Brahms was the Senior Design Engineer of the Theoretical Propulsion Group. (TNG: "Galaxy's Child")