No, there are no princesses in modern-day South Korea or North Korea.
While Korea has a rich history filled with royal families and dynasties, the last monarch of Korea, Emperor Gojong, abdicated in 1907, ending the Joseon Dynasty. With the abolishment of the monarchy, the title of "princess" no longer exists in Korea's political system.
However, there are several individuals who are descendants of the Joseon Dynasty's royal family and are sometimes referred to as "princesses" or "princes" by some members of the public. These individuals are typically recognized as descendants of the royal family, but they do not hold any official titles or privileges.
For example, Yi Hae-won, a descendant of the Joseon Dynasty, is often referred to as a "princess" by some people. However, she holds no official title and is simply a private citizen.
Therefore, while there are no official princesses in Korea today, there are individuals who are descendants of the royal family and are sometimes referred to as "princesses" by some people.
