Hello there! If you're interested, you can read my recent summary of Carthaginian government here. In short: Carthage was normally governed by its Senate and two annually-elected magistrates called suffetes ("judges"); a popular assembly, known simply as the People of Carthage, could debate, amend, and ratify proposals if the Senate and suffetes agreed to submit it to them or, according to Aristotle, if the Senate and suffetes were "not in agreement about a submission or non-submission" to the assembly. Another political body (which I did not mention in the linked post) was the Court of One Hundred and Four, whose official purpose was to prosecute returning generals for defeats, maladministration, treason, etc., though its influence seems to have extended to other areas of public affairs by Hannibal's time; it was apparently comprised of senators (or ex-senators?), and they held their position for life.

After Hannibal became suffete in 196--we unfortunately don't know the identity of the other suffete--he came into conflict with a financial official belonging to an opposing political faction. Hannibal had summoned the official for an inquiry (possibly regarding embezzlement), but the official refused on the knowledge that he was set to join the Hundred and Four and would soon be immune from legal scrutiny. So Hannibal arrested the official; he then expedited (or circumvented) the constitutional process by bringing a proposal directly to the People: "that the judges [of the Hundred and Four] would be elected for a single year each, and that no one would be judge for two consecutive years" (Livy 33.46.7). Election in this case would presumably be popular, in contrast to the previous system of co-option after a member of the Hundred died of old age. And Hannibal's proposal passed.

Our main source, Livy, doesn't really explore the implications of this reform, except that it mitigated corruption and earned Hannibal even more enemies than he had before. Historian Dexter Hoyos extrapolates, however, that the "[j]udges' hopes of success in this new judicio-political scheme would force them to be more open in their work, and prevent them from favouring aristocratic special interests too blatantly at ordinary citizens' expense. The senate in its turn... would lose their too-easily-exploitable symbiosis with the highest court of the republic and, moreover, would have to be more accountable to the rest of the citizen-body: for if prosecuted on serious charges a senator would find himself facing citizen-elected judges not at all guaranteed to be friendly." [1]

So there's a condensed version of Hannibal's reforms. Carthaginian political history is a rather tricky subject (due to a deficiency in sources), and I'm not sure if I could go into more detail without having to cover the political developments of the previous three centuries. I hope you find this helpful, nonetheless! :D

[1] Dexter Hoyos, Hannibal's Dynasty: Power and politics in the western Mediterranean, 247-183 BC (London and New York: Routledge, 2003), 192f.