Edmyn Tully is a character in Game of Thrones. He is long dead by the time depicted in the TV series. Lord Edmyn Tully was the Lord of Riverrun and a vassal of King Harren the Black, though he rebelled against him when Aegon the Conqueror invaded Westeros.
After the elimination of Harren and his entire line at the Burning of Harrenhal, Aegon rewarded Edmyn by elevating the Tullys to rule over the Riverlands (under the Targaryens), even though they had never ruled the Riverlands as kings – indeed, the Riverlands had been occupied by powerful neighboring kingdoms for centuries, and before that were rarely politically unified. Aegon made Edmyn Tully the first Lord Paramount of the Trident, a title his family held ever since.
In the books
In the A Song of Ice and Fire novels, Edmyn Tully’s backstory is the same.