Complex sentence: Despite its "Republic" moniker, the Centauri Republic is a nominal constitutional monarchy ruled by an Emperor or Empress, or, in the event of an interregnum, a Regent.
Split into simpler sentences: Despite its "Republic" moniker, the Centauri Republic is a nominal constitutional monarchy headed by an Imperial family. It is ruled by an Emperor or Empress, or, in the event of an interregnum, a Regent.