High Command is the ruling body of the Space Pirates. Although never actually seen in the Metroid games they are mentioned in various logs in Metroid Prime and Metroid Prime 2: Echoes. For instance they were the ones who ordered Ridley be rebuilt as Meta Ridley. High Command apparently supplies various Space Pirate outposts with troops, supplies, and orders, and they seem to be greatly respected.
In the Metroid Manga, Ridley, Mother Brain, and a Chozo named Gray Voice lead the Space Pirate organization with them attempting to get Samus Aran to join them. This group and the High Command mentioned in the Prime series may be different entities. One possibility is High Command runs the operations for the Space Pirates and are directly below Ridley, explaining how he was considered the Leader prior to Mother Brain.