A league was a group of sports teams that played against each other. One well known Earth example was Major League Baseball and its subdivision, Planetary Baseball League
In 2371, the Cestus Comets and Pike City Pioneers were members of a baseball league that included four other teams, with plans for two more. Their league did not use the designated hitter rule (having already considered but dismissed the idea), and favored wood bats over polyduranide. (DS9: "Family Business")
The term could also refer to a non-sports organization, as in the case of the Red-Headed League. (TNG: "Elementary, Dear Data")
In 2401, league was listed as one of the results in Raffaela Musiker's search for the "red lady". (PIC: "The Next Generation")