the Old World

SMART Vocabulary: related words and phrases

Countries, nationalities & continents: continents & regions of the world
Afrocentric
Afrocentrism
amazonian
Antarctica
Antipodean
black Africa
gulf
interhemispheric
Lapland
LATAM
Latin America
meridian
parallel
pole
the Antipodes
the International Date Line
the Pacific Rim
the South Pole
the subtropics
the Tropic of Cancer

Examples from literature

Europeans first learned of it when explorers came to the New World around 1500. 
Spain claimed the New World as its territory. 

New World | American Dictionary

New World
noun[ U ]
us/ˈnu ˈwɜrld/
North, Central, and South America, as they were considered by the Europeans after Christopher Columbus traveled there

Note:

The phrase "Western Hemisphere" is generally preferred.