What kind of institution is Gotei 13? Authority? Justice? Policy maker?
The Gotei 13 was mainly used to keep the control and order in the Soul Society. They are also the first line of defense from any enemies, such as Hollows, Quincies, etc. They maintain the balance between the spirit world and the real world by eliminating Hollows, and guiding lost souls. 

The main purpose of the 13 was to provide an authoritative sense. Hope this answers your question.