The Galactic Republic is an organization set up to control the diplomacy in the Galaxy Far Far Away, and since its establishment after the collapse of the Sith Empire at the hands of Trask Ulgo, Carth Onasi and Rarth Devan, the Republic has swelled to encompass nearly all of its Galaxy.At start of the Clone War, the splinter faction known as the CIS attempted to bring down the Republic and defy the League. The Galactic Republic fought back with an Army of Clones, which eventually destroyed the Republic and forged the Galactic Empire.
The Republic was briefly vanquished by Darth Vader and replaced with the Galactic Empire, which corresponded with the fall of the Jedi Order. However, both the Order and the Republic recovered soon afterwards. The corruption of the Sith brought about by the Supreme Chancellor never really left the Republic, however.