Her "emerging anew" was more to do with a state of mind. From the jist of things, the Dual Awakened is devoid of any thought, emotion or desire whatsoever. A whole lot of power and emptiness. From that description, it seems comparable to a black hole.

Clare avoided being absorbed into by retaining her ego, it seems. Maintaining her sense of self prevented her from turning into a mass of nothingness.

If it was a power that got her out of it, I'd call it willpower, as opposed to physical prowess which you seem to be hinting.

Of course, she owes a huge thanks to whoever that voice was.