East Hyrule is the part of Hyrule, that became the part of Squadala Empire after Hyrulian Civil War. Current leader of East Hyrule is Ducky. This country is allied with Ducky Empire, which in-between was the main operations base for ZioraTek Machinery, LLC Ltd..
East Hyrule is big desert land, with very hot climate. It's the closest thing you'll get to the Squadala Empire in Europe. There are many castles, but most of them were destroyed by The Evil Forces of Ganon.
Originally it was the part of Hyrule, ruled by The King. But when Hyrulian Civil War started, most of territories became the parts of Squadala Empire. The King had no choice and gave East Hyrule to Morshu. Later, it became part of the Ducky Empire, but ceased to exist in the slow, brutal, deliberate Second Hyrulian War.