How did pope paul 3rd set out to revive the moral authority of the church and stop the spread of protestatism

Pope Paul III approved various measures which have been referred to as the "Catholic Reformation" or "Counter-Reformation."

The Catholic Reformation or Counter-Reformation was an effort by the Roman Catholic Church to strengthen itself in response to the Protestant Reformation.  Here are some of the aspects of that movement in which Pope Paul III was involved:

Religious orders were founded that aimed to build allegiance to Rome and the papacy, and to educate people in Catholic teaching.  The Society of Jesus, known as the Jesuits for short, was a key order of this sort.  The order was founded by Ignatius of Loyola in 1534, along with Francis Xavier and several others.  It aimed to affirm the full authority of the pope as leader of all the church and educate people properly in Catholic doctrine.  Paul III gave his official papal approval to the Jesuit order in 1540. In 1542, Pope Paul III established the Congregation of the Holy Office of the Inquisition, which we usually refer to simply as The Roman Inquisition.  It acted as an investigative body in regard to threats to Rome's teachings.The Council of Trent served to reform some abuses that were acknowledged by the Catholic Church, and especially served to assert the full authority of Roman power and doctrine over the Protestant threat.  The Council of Trent held meetings over a span of years from 1545 to 1563.  Pope Paul III called for the Council of Trent to be held and presided over it during its first eight sessions. (He died in 1549, and further sessions continued to be held in years after that.)