* νέα ἀρχή (nea archē): This is the most literal translation, meaning "new beginning." It's a good general-purpose option.
* καινή ἀρχή (kainē archē): This translates to "new beginning" as well, but "kainē" implies a more radical, transformative new beginning, a fresh start that is qualitatively different from what came before. Think "a whole new chapter."
* ἀναγέννησις (anagénnēsis): This word means "rebirth" or "regeneration." It suggests a new beginning that arises from something old, a renewal or resurrection.
The best word to use will depend on the context.