Pete Vance is the third Vance brother(maybe born in 1958-Lance's date of birth- or later) who is mentioned in Grand Theft Auto: Vice City Stories. He never appears, but is a key character. Though he does not have a part in the game, he is mentioned at the start by Victor and mentioned later by name by Lance. Pete suffers from asthma and Victor joined the army so he can get money for Pete's medicine.
Before Rockstar's confirmation about Vic's death in GTA Vice City, there were rumors that Vic did not die but instead, Pete died. An argument for this is the inconsistency of using different voice actors but this can be rebutted with the example of Toni Cipriani having different voice actors. Evidence supporting Vic's death was Vic's name and his involvement with Lance on Rockstar's site for GTA VC.
It is unknown what happens to Pete after VCS. It is most likely that he lived a normal life after Vic paid for his medicine. As of 1986, he is the only surviving member of the Vance family.