Actually, the Republic had a form of succession with two Tribunes. The Empire didn’t.
The so-called Republic had two *consuls*, who served for a single one-year term, and could veto each other’s decrees. It was a way to keep a balance of factions among the 35 or so families who literally owned Italy and most of the population of Rome itself.
Tribunes were as numerous as the tribes, and as the tribal identity faded away in the 1st & 2nd c AD,
10 tribunes, two consuls, a varying number of praetors and a bunch of minor magistrates, all elected for annual terms.
A term-limited Dictator in ultimate emergency.