An engineering team was a specialized away team sent to assist with technical matters.

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 2063, Geordi La Forge led an engineering team, Alpha team, who were assigned to assist Zefram Cochrane repair the Phoenix after a Borg attack. (Star Trek: First Contact)

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 the attack that enabled them to capture the starship in 2374. (DS9: "One Little Ship")