During which empire was the Indian region divided into territories, controlled by officials, while regions that were conquered outside of the empire were controlled by local leaders adhering to empire rule?

The correct answer to this is:

This happened during the "Gupta Empire".

The period in which the Gupta Empire existed was also called the Golden Age of India. This is because during this time, peace and harmony was created under the leadership of the Guptas. This also enabled the search of scientific and artistic endeavors.