The Federation has had its share of run-ins with the organization. For example, Deanna Troi was once altered surgically by the Romulan underground to resemble Major Rakal of the Tal Shiar (TNG episode "Face of the Enemy", season 6).
Tal Shiar and Obsidian Order had an alliance to destroy the Dominion.
Some soldiers accuse the Tal Shiar being the ones who would bring the downfall of the Romulan Star Empire, not the military.