That would usually mean leaving behind everything of the past, and starting with a zero, as Tracy Chapman says.
One might say it’s a rejection of all that exists, leaving it all behind, and seeking all that is new, better, and preferred. But even in this fresh start, there is always the presence of the old, even if it is as just a building block, from which you take flight. You don’t just drop everything.
Or, there is no new thing in a fresh start, it’s just looking at the old in a different way; in a way that offers a different perspective to serve a different purpose.
A fresh view, perhaps, rather than a fresh start.