A systems engineer was a type of engineer who specialized in starship subsystems, such as transporters.
In 2286, the USS Yorktown's systems engineers put together a solar sail in the hopes that it would generate enough power to keep the crew alive. (Star Trek IV: The Voyage Home)
Lieutenant Reginald Barclay was one of several systems engineers serving aboard the USS Enterprise-D during the late 2360s.
In 2369, Lieutenant Commander Geordi La Forge required a systems engineer to assist in bridging the transporter systems between the damaged USS Yosemite and the Enterprise. When La Forge mentioned this to Barclay, who had a fear of transporters, Barclay attempted to pass the assignment off to Ensign Dern, however, La Forge clarified that he meant for Barclay to join. (TNG: "Realm of Fear")
The same year, Lt. Pierson was assigned to the systems monitor room aboard the Enterprise-D. (TNG: "The Quality of Life")
The systems engineer aboard the SS Vico was the mother of the lone survivor found aboard the ship, a boy named Timothy. (TNG: "Hero Worship")