Here we are coming upon the last of the 3D Universe GTA games, the ones that as far as I can tell very few talk about, possibly due to being PSP games initially that were ported to console later on. The game itself takes place in 1998, 3 years before the events of GTA III. You play as Toni Cipriani, the capo of the Leone family. Toni was an arguably minor character in III who gave missions to Claude which targeted the Triads specifically and did nothing else. In this game, Tony has to regain don Salvatore Leone's trust and earn the title after some time away. I do not remember the specifics of why Toni left in the first place, though. The primary way in which you do this is by getting Leone out of trouble when needed and destroying the other mafia families in Liberty City, the Sindacco and the Forelli families as well as a family just called the Sicilian Mafia. In the process, the Leone family becomes the primary mafia family in the city and the distribution of the gangs in Liberty City ends up as seen in III.
The game itself is your standard GTA fare while having more in common with III in terms of mechanics: no swimming, no flying vehicles and the like. There are new minigames and side missions and things but not much outside of that. The radio stations in the game are the same as in III with the exception of one being that Chatterbox is now a program on a larger talk show station. I listened to Double Clef and the talk station exclusively. It's just your average GTA game and is enjoyable. Go for it if you wish.