Instead of reaching a new world they only got their feet wet and splashed their legs for the second time that morning (if it was a morning: it seems to be always the same time in the Wood between the Worlds).
As the bright young stars of that new world came out they talked over everything: how Digory had hoped to get something for his Mother and how, instead of that, he had been sent on this message.
Then Digory knew that all the Narnians had heard those words and that the story of them would be handed down from father to son in that new world for hundreds of years and perhaps forever.
There are no more uses of "New World" in the book.
Show samples from other sources
The way these poets are able to lure you into a whole new world, viewing things from a vantage point you’ve never seen before.
Colleen Hoover -- Slammed
The air was crisp and cool and the forest felt fresh, like he was standing in a brand-new world—a place untouched by disease.