Insei

, also known as "cloistered rule," is an ancient Japanese term which means a special form of Imperial government. 
In the "Insei" system, the monarch abdicated or retired and a new emperor was named; however, the old emperor held on to significant power and influence in the court and in the nation. The emperors who withdrew from public life did not give up any of their many powers. In practice, the retired emperor only gave up the time-consuming burden of his ceremonial roles and formal duties.
There were emperors who abdicated before and after the Heian period; however, the term "Insei" is most often used to mean the kind of Imperial system put in place by Emperor Shirakawa in 1086. This system was very important in the years before the rise of the Kamakura shogunate in 1192. 
Heian period.
The succession of power in the "Insei" system was complex.
Edo period.
The last retired emperor with an "Insei" title was Emperor Reigen in the Edo period.