Why are there new airbenders in Avatar? In the spin-off of Avatar: The Last Airbender, Avatar: The Legend of Korra, we learn in the second season that the bending is a gift from the Lion-turtles.

However, during season 3, there are new airbenders due to Harmonic Convergence.

Why then there are not new water/fire/earth benders?
Harmonic convergence led to great change that did more than provide a pathway between the two worlds. Since the fire nation had previously wiped out most air benders, there was a great imbalance among the four nations. There was a natural rebalancing that occurred as a result of harmonic convergence which led to an awakening for air benders only. Since Korra said this was how the world was supposed to be, a good reason for that would be that the spiritual energy helps keep a balance among the four nations and bending types.