The Klingon Second Empire was led by Chancellor Mow'ga.
During his reign, he ordered a fleet of Klingon warships to invade and conquer the Breen. The fleet was never heard from again. (DS9: "'Til Death Do Us Part")
The Klingon Second Empire is not associated with, nor should it be confused with, the Second Dynasty. It was presumably preceded by the Klingon First Empire, and Worf's use of the past tense when talking about it suggests that it was a different entity from the 24th century Klingon Empire.
Due to Chancellor Mow'ga's apparent authority, the Second Empire is likely set after the reign of the last Emperor ended in the mid-21st century