An engineering team, engineering crew, engine crew, engineering detail, or engineering staff were engineers– individuals proficient in engineering matters– that assisted a chief engineer. These teams worked in main engineering and were often called up to assist a landing party or away team,
In 2063, Geordi La Forge led an engineering team, Alpha team, who were assigned to help Zefram Cochrane repair the Phoenix after a Borg attack. (Star Trek: First Contact)
Following the deactivation of Vaal, Kirk ordered an engineering detail with full analytical equipment and beam them down. (TOS: "The Apple")
In 2368, the USS Enterprise-D beamed down an engineering team to assist the Moab IV colonists in installing a structural support system. (TNG: "The Masterpiece Society")
In late 2373, General Martok requested an engineering team from Deep Space 9 to be waiting when the IKS Rotarran docked to begin repairing its battle damage. (DS9: "Soldiers of the Empire")
A Jem'Hadar engineering team was able to restart the impulse engine of the USS Defiant, after they had been damaged in an attack that enabled them to capture the starship in 2374. (DS9: "One Little Ship")