The Trelonian government was the government of the Trelonians.
General Yiri was confronted with a question of loyalty after his brother was accused of betraying the government, following the discovery of circumstantial evidence. Would he protect his brother or protect the state? Yiri chose the state, with his brother being executed. This event from the internal affairs of the Trelonians was a topic of conversation for Elim Garak and Julian Bashir in 2370. (DS9: "Profit and Loss")
According to StarTrek.com, Trelonians were from the planet Trelonia. [1](X)