The Sheliak Corporate was the official governing body of the Sheliak.
In 2255, the Sheliak Corporate was involved in a brief conflict with the United Federation of Planets. Eventually, the conflict was resolved with the signing of the Treaty of Armens. Obtaining the treaty was a difficult process, as the Sheliaks' noted value of precision made the treaty long and complicated, and meant that a large team of Federation representatives had to oversee the signing of the treaty.
In 2366, a dispute broke out between the Federation and the Sheliak, when the Sheliak discovered Federation colonists living on Tau Cygna V, a planet which they wished to colonize. By the terms of the treaty, the Sheliak reserved the right to demand the removal of the colonists. Eventually, the matter was resolved by the crew of the USS Enterprise-D, and the colonists were removed. (TNG episode: "The Ensigns of Command")
A Sheliak was along representatives of many Alpha and Beta Quadrant powers gathered to help create and deliver the Temporal Defense Grid entirely in secret by the 25th century. (DTI novel: Watching the Clock)
Lieutenant Nog was able to procure shield modulator technology for the Sheliak designed to improve shield efficiency against radiation. It was deployed on the evacuation fleet sent to Europa Nova during the Gateways Crisis. (DS9 novel: Demons of Air and Darkness)