If Hannibal succeeds in totally destroying Rome and its inhabitants, he will also need to destroy a number of colonae and cities in Latium, Etruria, Campania, Picenum and Umbria, to prevent the leaders of these external Roman centres from reforming the Republic. Hannibal would need to make sure that the newly independent Socii states in Italy crackdown on their former Roman overlords.
After that, Hannibal may next sail to western Sicily, to restore Carthage's authority over the former Punic colonies there. If the sack of Rome occurs before the year 212 BCE, than Carthage's dominance of the whole island may be challenged by its oldest rival: Syracuse.
Syracuse was sacked by the Romans in 212. Before that it was a very rich and formidable city-state. Syracuse was not just a contender for local dominance, but was right in the path of major traffic from the eastern Mediterranean. Most ships from the east would pass through it's ports before reaching Carthage. And if left unchecked, could form a league out of the other Greek colonies, not just in Sicily, but on the Italian mainland as well. But if Hannibal destroys Rome after 212 BCE, all Sicily could be brought under nominal Carthaginian rule in a few years.
But Carthage would still have a long way to go before properly competing on the world stage again, and may not be able to pull it all off within Hannibal's lifetime. Not to mention that Hannibal was still the governor-general of Carthage's territories in Iberia, and governed on his own terms, but "in the name of Carthage". There may be a reckoning between Hannibal's partisans and the Carthaginian senate.