Avatar Maikki worked for the Republic City Police Force for a long time before she discovered that she was the Avatar. She had been so focused on perfecting her metalbending that she hadn't even considered anything else. Not even the fact that she was born the very day the previous Avatar, Korra, died.
She realized who she was one night while chasing down a dangerous criminal. She was injured badly and her instincts sent her into the Avatar State to keep her alive.
Maikki was immediately taken to Air Temple Island to train with the airbenders and the White Lotus there.