The crossword solutions for the term 'Successor of Claudius' are Nero (4 letters) and COST (4 letters). Nero was the fifth Roman Emperor, succeeding Claudius in 54 AD. He is remembered for his extravagance and debauchery, as well as his persecution of Christians. COST was a Roman Emperor who succeeded Nero in 68 AD. He was known for his military prowess and for restoring stability to the Roman Empire after Nero's reign.