Answer:
Legalism remained in effect throughout the Qin Dynasty until its fall in 206 BCE. After the Qin had fallen, the states of Chu and Han fought for control of the country until Xiang-Yu of Chu (l. 232-202 BCE) was defeated by Liu Bang of Han (l. c. 256-195 BCE) at the Battle of Gaixia in 202 BCE and the Han Dynasty was founded. The Han Dynasty reigned for a long time, from 202 BCE to 220 CE, and began many of the most important cultural advances in Chinese history, the opening of the Silk Road being only one of them.
They originally kept a form of Legalism as their official philosophy but it was a much gentler version than that of the Qin. The Emperor Wu (141-87 BCE) finally abandoned Legalism in favor of Confucianism and also made it illegal for anyone who followed the philosophies of Han Feizi or Shang Yang to hold public office.
Confucianism could be expressed openly again during the Han Dynasty. The suppression of Legalism and Legalist philosophers diminished the threat of the philosophy taking hold again and allowed for opposing views to be explored. This did not mean that Legalism disappeared or that it no longer had any effect on the Chinese culture, however. Legalism remained a go-to philosophy throughout China's history up into modern times. Whenever a government has felt it might be losing control it has resorted to some degree of Legalism.
The days of the supremacy of Legalism in China were over, though. Koller writes, "the long-term effect of the Legalist emphasis on laws and punishment was to strengthen Confucianism by making legal institutions a vehicle for Confucian morality" (208). The vacuum left by the rejection of Legalism was filled by Confucianism which provided the Chinese culture with a much more comfortable and all-embracing vision of humanity and how people could live together peacefully.