The Jedi were integrated into the Republic as a peacekeeping/ humanitarian/ advisery organization after Darth Bane more or less wiped out the Sith Brotherhood and much of the Jedi led Army of Light at the end of the New Sith Wars. Though both before and after the New Sith Wars there were points where there were Jedi chancellors or even the Jedi de facto taking over when the Republic more or less collapsed a couple time, not even getting into military leader like Revan, Surik, or Lord Hoth who held military positions within the Republic.
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The Jedi were integrated into the Republic as a peacekeeping/ humanitarian/ advisery organization after Darth Bane more or less wiped out the Sith Brotherhood and much of the Jedi led Army of Light at the end of the New Sith Wars. Though both before the after the New Sith Wars there were points where there were Jedi chancellors or even the Jedi de facto taking over when the Republic more or less collapsed a couple time, not even getting into military leader like Revan, Surik, or Lord Hoth who held military positions within the Republic.