NATO was an Earth-based organisation.
A rogue NATO commander was killed by an Ogri in Little Caldwell. This stopped NATO from discovering that the commander was responsible for abducting both aliens and humans. (PROSE: Return of the Living Dad)
A clone of Martha Jones created by the Sontarans used the memories of her counterpart to access the NATO Defence System and cancel attacks made against the Sontaran ship in orbit above the Earth. (TV: The Poison Sky)