Studio Mir, the animation company responsible for Legend of Korra, responded to some Korra relevant questions on their Facebook page. Of course, many of the questions were revolving around the release of Book 3.
While the Korean studio did not have an exact release date, they did tell us that they have already finished animating season 3. They went on to confirm that Book 3 will be releasing very soon.
In fact, it already seems quite likely that the season will air this summer, according to a recent news publication by Breathecast. Looks like for now, we'll just have to wait for Nickelodeon's word.