By Catholic Answers, Staff - Catholics believe that the pope is the vicar of Christ and successor of St. Peter, the visible leader of the universal Church, against which Jesus promises the gates of hell will never prevail (Matt. 16:18-19). After a pope dies or resigns, a papal conclave commences within three weeks to elect his successor. A conclave is the gathering of the College of Cardinals in which these papal electors choose the next pope.. The Process of Electing a Pope in the Catholic Church ....