Alternate Reality(split 2233)
An Air Defense Team was a specialized group of Starfleet personnel on Earth, in the alternate reality, which deal with airborne attacks.
In 2259, when John Harrison began to attack the senior staff assembled in the Daystrom Conference Room at Starfleet Command, admiral Christopher Pike requested such a team to assist. (Star Trek Into Darkness)
It was not explicitly said if the air defense team was a part of Starfleet, though is assumed here because Starfleet is usually responsible for the defense of their own installations.