The Senate was not a structure defined by the Western or Eastern Roman Empire, It existed within them. It also existed when Italy was ruled by the Osthrogoths and Lombards.

So yes, there was not only a Senate in the later Eastern Roman Empire, while East Rome controlled Italy, the Senatorial class of Italy and their Senate was also part of East Rome.

While the Roman Senate (Senate of Rome/Italy) itself disappears by the 7th century, East Rome retained its own senate for its own region.