An emergency team is a specialized group of Starfleet personnel formed to deal with emergency situations aboard Federation starships and space stations. Members from the medical staff are usually part (or all) of the team, which led to the often use of the terms medical emergency team, emergency medical team, or simply medical team. The team would usually traverse to the origin of the emergency and provide on-site assistance to try and stabilize the situation, and injured personnel may have required additional attention in a medical facility, such as sickbay. Occasionally, medical personnel were requested by simply asking for medical assistance instead of explicitly requesting an entire team, but the desired outcome was the same.
Captain Jean-Luc Picard called for a medical emergency team to transporter room 16 when Commander William T. Riker, Lieutenant Commander Data and Lieutenant Worf were beamed back to the USS Enterprise-D. (TNG: "We'll Always Have Paris")
Riker called for medical assistance to the bridge when an crewmember was seemingly injured during one of the attacks by the Delta Rana warship. (TNG: "The Survivors")
Data called for medical assistance to Main Engineering when Q experienced back pain. (TNG: "Deja Q")
Riker told Captain Rachel Garrett of the USS Enterprise-C that emergency teams were boarding the vessel to assess the damage done to it after the battle with Romulan warbirds at Narendra III. (TNG: "Yesterday's Enterprise")
As part of the release of hostages in Ten Forward being held by the aliens inhabiting members of his crew, Picard called for an emergency medical team from Sickbay to accompany him to Ten Forward. He later called for a team to the cargo bay when the aliens were transported away. (TNG: "Power Play")
Garak called a medical emergency team to his shop after Odo collapsed on the floor. (DS9: "Broken Link")
The Emergency Medical Holographic program was one of Starfleet's initiatives to provide medical assistance in dire circumstances, but was normally limited to only areas that supported holographic projections, such as sickbays aboard Intrepid-class starships. (Star Trek: Voyager)
Picard called for a medical team to the bridge of the USS Enterprise-E after a hull breach had been created during the battle with the Scimitar. (Star Trek Nemesis)