Based on this article from Vine Report, Sword Art Online “season 3” will most likely be release on Summer 2016. Reason being is because after the announcement of the film project, the anime staff will be focusing on the film rather than this new anime. Season 3, also known for the Underworld arc, will be quite different than the past games because the world in the game is an AI Simulation. Here is what it’s described as:
The characters are expected to end up in a Renaissance themed world where they will be charged with building their own region using an advanced technology.
It was expected online that the anime season was going to start at the end of 2015 and go up to 2016, but since the announcement of the film, it will have to wait. It is also confirmed that there will also be a season 3 and 4, Underworld and Alicization, and it will have new characters like Eugeo and Alice.