The New Republic is a government organization in the Star Wars universe that arose after the death of Emperor Sheev Palpatine and the redemption of Anakin Skywalker.
Canon Continuity
Following the victory at the Battle of Endor the Rebel Alliance formed a new government called the New Republic. Just over a year after the Battle of Endor the New Republic engaged Imperial forces on the far off world of Jakku, defeating the Imperial fleet there and leaving the remains of a number of startships scattered over the planet.
Legends Continuity
As in the canon continuity the Rebel Alliance organized itself into the New Republic following the Battle of Endor. Two years after the Battle of Endor the New Republic retook Coruscant. It is known Mon Mothma and Princess Leia became their chiefs of state.
During the height of the Yuuzan Vong War, the New Republic was reorganized into the Galactic Federation of Free Alliances.