The primary duties of a Tetrarch are administering a local region in a similar manner to a Consilium or otherwise policing the Seers of the Throne and enforcing the Lie. They have risen through the ranks and mysteries of the order, survived and flourished in an environment of some of the most vicious political infighting in the world. While the average Pentacle Hierarch achieves his position through cannily outmaneuvering his rivals and establishing sufficient allies to defend himself from attack, a Seer attains the position through brutally undercutting and overcoming (sometimes destroying) his rivals and ensuring that his allies have been sufficiently cowed into supporting him without seeking to supplant him. The Exarchs don’t reward friendship and loyalty, only the unabashed will to power, so politics among the Seers tends to be significantly more cutthroat (literally) than among the Pentacle orders. Communication remains a primary responsibility of the tetrarchs. Each serves not only to relay communication from the Ministers above to the pylons below, but also to coordinate initiatives between the Ministries active in the region. They also work to ensure orthodoxy within their own Ministry while simultaneously striving to induce Seers of other Ministries from their own paths.
All Tetrarchs are extremely powerful mages (as otherwise, they would have never been able to obtain the title), some have even risen to archmastery and founded Legacies. Many are also firmly entrenched into Sleeper society and wield considerable influence among the un-awakened.
A Tetrarch in turn answers to a Minister.