They were famed for their artistic and design skills, and for their large families; there was an Outworld joke that if the Kavethssu ran the Empire, there would be no need for weapons to conquer neighboring worlds - they would simply overrun them by sheer numbers.
In the early 23rd century the Empire relocated them to distant colonies including Mirhassa and Ssuvat, in an attempt to silence their outspoken criticism of the government. In response, they began actively plotting the overthrow of the Imperial government. Members of Clan Kaveth on the Two Worlds and elsewhere seem to have acted as an unofficial spy network for the rebels in the Romulan Civil War. Their chieftain-designate in 2276 was Thala tr'Kaveth. (TOS - Rihannsu novel: The Romulan Way)