Three years pass between the end of Book 3: Change and the start of Book 4: Balance. The time jump is central to Korra's physical and emotional recovery.
Book 3 ends after Zaheer poisons Korra with mercury and forces her into the Avatar State. Although she survives, the battle leaves her severely injured and deeply traumatized. By the beginning of Book 4, Korra has spent most of the intervening three years at the South Pole, undergoing rehabilitation and struggling to reconnect with her identity as the Avatar.
During this period, Korra remains in contact only with Asami, who writes to her regularly. Korra's absence also allows the political situation to change dramatically. Kuvira rises as a powerful military leader and begins reunifying the fractured Earth Kingdom through increasingly authoritarian methods. Meanwhile, the Air Nation and Korra's friends continue working without her direct involvement.
The three-year gap explains why Korra looks older and why Book 4 begins with her unable to fight effectively. It also creates a deliberate contrast with the rapid pace of earlier seasons. The story is not picking up immediately after Zaheer's defeat; it begins after a long, difficult recovery that Korra has largely faced away from the public.