St Peter's Church, especially the one in Rome which forms the Vatican, has a long and storied history. However, if you're referring to a specific St Peter's Church, such as one in a different location, the answer might vary. For St Peter's Basilica in the Vatican, one of the most significant periods of change in clergy came during the Renaissance and the Reformation, especially in the 16th century.

During this time, the Catholic Church was undergoing significant transformations and challenges:

1. The Reformation: This period witnessed significant religious and political upheaval, leading to the Protestant Reformation. Accusations of corruption among church leaders and the sale of indulgences were central issues that led to calls for reform and a turnover in church leadership.

2. The Council of Trent (1545-1563): This was a major part of the Counter-Reformation in which the Church sought to address and reform many of the issues raised by Reformers. New bishops and priests were often appointed to replace those who were seen as corrupt or ineffective.

3. The Renaissance Papacy: Several popes during the Renaissance were known for allegiances to political families, leading to significant turnover and appointments within the Church.

For a more precise timeline related to a specific St Peter's Church, it would be helpful to know its exact location or any other cues, as local events can also significantly affect clergy appointment and turnover.