Biologist
Emperor
Augustus?
Yes, there ya go!
Time to explain my rather obscure clues:
1.) Since the play has been so good, clap your hands; all of you dismiss us with applause.
These were Augustus's (Octavian's) last words. They referred to the fact that he maintained the charade of running a Republic, despite the republican power structure having been mostly destroyed or made ceremonial.
2.) Not the beginning of the end, but the end of the beginning.
Octavian's death was not the end of the Republic era (that started with the civil war between Sulla and Gaius Marius), but the prelude to the Imperial era of Roman history.
3.) The lackey and the priest have been dealt with; now to find an heir.
"The lackey" is Mark Antony, Julius Caesar's former lieutenant; "the priest" is Lepidus, the Pontifex Maximus during Octavian's power struggle with Antony. Octavian himself had no heirs, and had to adopt one (Tiberius).
4.) Emperor in all but name.
Augustus was actually a title, but it didn't mean "Emperor". The closest titles were "Imperator" (military chief) and "Princeps" (first citizen or prince).
5.) The Senators have all been sidelined.
This is self-explanatory. The Senate had ceased to be more than a ceremonial body by the end of Octavian's rule.
I could have made this a lot easier, but any direct references to Rome/Latin/Italy would have given it away too quickly. Sorry I had such a hard time narrowing it down for you guys.