Connaught Rossa was the mother of Lieutenant Commander Connor Rossa, mother-in-law to Moira Rossa, and grandmother of Jeremiah Rossa. She lost both of her sons in skirmishes; Connor Rossa and his wife were killed during the Galen border conflict on Galen IV and her second son died during a battle at the Krasner outpost. She considered herself part of a family that had fought for many generations to bring peace to the galaxy.
In 2367, the USS Enterprise-D rescued Jeremiah Rossa, previously believed to have been killed on Galen IV, from a disabled Talarian observation craft. Upon discovering this, Admiral Rossa sent a subspace message to Jeremiah aboard the Enterprise, expressing her excitement that he was alive and her anticipation of his return home, knowing he was the last in her family line. However, Jeremiah had no desire to do this and elected to remain with his adopted Talarian family. (TNG: "Suddenly Human")
Admiral Rossa was played by actress Barbara Townsend.
The script for "Suddenly Human" gives the pronunciation of Rossa's name as, "cn-NAWT ROW-sa" and goes on to describe her as, "a woman in her 60's, of regal bearing and gracious manner." This would put her year of birth at sometime during the 2300s. 
Rossa appears in the Star Trek: Section 31 novel Rogue, in which she orders the release of Commander Cortin Zweller on the charge of violating the Prime Directive, despite objections from both Admiral Marta Batanides and Captain Jean-Luc Picard. This leads them to suspect that Admiral Rossa has something to do with the rogue agency, Section 31.