In the Disney canon, there are three galactic Republics in history that we know of:
The Old Republic, which we have no idea when was founded. Sometime in the mists of history.
Around 1000 years before Attack of the Clones, the wars between the Old Republic/Jedi and the Sith came to an end, and the Old Republic evolved into the Galactic Republic. The Galactic Republic stood until Palps reorganized it into the Galactic Empire.
Finally, most recent is the New Republic, founded shortly after ROTJ and either in tatters or completely gone as a result of Starkiller Base’s attack in The Force Awakens.