- You may be looking for Gallifrey's family units or political chapters.
Gallifreyan chapterhouses, sometimes called simply Houses, were the sentient homes of the Great Houses. (PROSE: Lungbarrow, The Book of the War, Against Nature) They were the oldest living things on Gallifrey; the first ones were grown during the Intuitive Revelation. (PROSE: Lungbarrow)
Description
Houses were grown from seeds, and the walls of each House resembled tree trunks growing very close together. (PROSE: Lungbarrow) Since childrene were Loomed fully grown, (PROSE: Lungbarrow, Against Nature) the architecture and furniture of Houses resembled scaled-up versions of ordinary buildings, with the intent that the residents would feel small in comparison. The oversized wooden furniture, engraved with animal motifs, was also grown as part of the House, and the pieces had their own sentience; for instance, the Seventh Doctor warned a chair in the House of Lungbarrow to stay quiet.
Houses were aware of everything that happened inside of them, and they could communicate with inhabitants by opening or shutting doors, shifting interior walls, and moving on its foundation. The Housekeeper was in charge of maintaining the House's health and happiness; the House could communicate with or through the mind of the Housekeeper. (PROSE: Lungbarrow)
Each chapterhouse contained its Great House's breeding-engine, often kept in a loomshed. (PROSE: Lungbarrow, The Book of the War) Every Great House shared an essential tie with its chapterhouse; if the chapterhouse fell into neglect, the House itself would unravel. Chatelaines from other Houses were often assigned to maintain chapterhouses whose Great Houses had fallen into obscurity. (PROSE: The Book of the War)
Drudges were servants within the Houses. (PROSE: Lungbarrow, Against Nature)
By one account, the term "chapterhouse" was specifically reserved for the headquarters of the Chapters; (PROSE: Lungbarrow) by other accounts, all homes of Great Houses were called chapterhouses. (PROSE: The Book of the War, Against Nature, et al)
Examples
The House of Lungbarrow was grown into and named for Mount Lung. Despite being banished, the Doctor visited it in his seventh incarnation. (PROSE: Lungbarrow) The Eighth Doctor remembered his father discussing plans with Mr Saldaamir in the Great Hall of Lungbarrow. (PROSE: Unnatural History)
The great hall of House Catherion's chapterhouse became known as the Hall of Faces after an escaped babel slaughtered all of the residents. (PROSE: The Book of the War)
An owl statue guarded the gate of the Prydon Chapterhouse. (PROSE: Lungbarrow)
The High Council hid the dangers of regeneration from the general public by confining victims to secret Shadow Houses. (AUDIO: Trial of the Valeyard)
Chatelaine Thessalia took care of House Ixion's abandoned chapterhouse and transformed it into the headquarters for her Order of the Weal. (PROSE: The Book of the War) It was located on the edge of the Homeworld's southern mountains. (PROSE: The Return of the King)
Romana grew up in the House of Heartshaven, where the paintings on the walls would whisper and the lamps of the great hall would light up when the heirs to the House would enter. However, when she returned there after the Gallifreyan Civil War, she found it abandoned and infested with pig-rats. Shortly thereafter, the House burned down. (AUDIO: Panacea)
The Rivera Manuscript described a renegade's praxis-induced vision of the enemy's attack on the Homeworld at the start of the War in Heaven. In that vision, supercharged chunks of the causal nexus materialised in the sky as black fireballs and crashed into the chapterhouses of the Homeworld. (PROSE: The Book of the War)