After the outbreak of World War I on August 1914 the government of Italy declared neutrality.
Even though the Triple Alliance still happened to be in effect what incentive did the Triple Entente provide that eventually led Italy to join on the side of the Allied Powers? Although Austria-Hungary held on to irrendenta such as Trieste and South Tyrol couldn’t they have renegotiated disputes over these territories in order to ensure their entry into the war alongside the Central Powers?
Pretty much what you said. There was territory Italy wanted that was part of Austria-Hungary. The Allied powers had no problem with promising this territory to Italy; they weren’t giving up their territory. The Central powers were more limited; they had to balance Italian and Austro-Hungarian desires.
Italy had no significant territorial desires in SE France at the time. But they DID have some significant issues with Austro-Hungarian holdings to their NE. They had signed an agreement with France in 1902 that they kept secret, which was probably incompatible with their duties under the Triple Alliance.
A series of negotiations and counter-negotiations occurred after the Italians refused to enter the war (claiming that the Alliance was defensive in nature, and the Germans and Austrians had been the attackers). Britain and France offered the Italians quite a lot, much more than they actually got, IIRC. In contrast, the Austrians and Germans didn’t offer very much at all in the way of concessions. That was probably a mistake on their part, as opening a southern front against France would likely have caused a significant change in the dynamics of the stationary front between the Germans and the Entente in Belgium/France.