"...how to re-establish the Republic?"
We cannot. The transition from Stone Age to Space Age technology is complete, and the roll out of decentralized means of production is ongoing. Centralized collective industry and political mechanisms can no longer dominate individual production and policy, and such collective mechanisms will only become weaker as individuals become stronger over time.
Anarchic society will eventually be the only possible choice, particularly as humanity spreads across the universe where armies of thugs cannot follow and project force. The sooner we adopt the decentralized means of production of the necessities we require and the blessings of civilization we desire, the sooner the abuses of tyrants will end. The cycle of revolution and re-imposition of tyranny over time will no longer be possible because the laws of physics mandate that decentralization of the means of production is now the cutting edge of technological advance, and productivity of collective production or political organization can no longer compete with modern means.
The future is freedom, prosperity, and the expansion of life across the infinite barren wastes of the universe. Paradise is coming, as has long been prophesied by wizened seers and is promised by our posterity. Humanity will be restored to the egalitarian society that is created by individual households themselves producing their necessities, eliminating overlords and armed gangs of thugs as parasitic losses are eliminated to increase productivity.
Thanks!