Galatians 2:16 says we are saved by; ‘The faith of Jesus’ and not by our works of the law.
In the case of Zaccheus in Luke 19:-10, it was the revelation that Jesus is the Son of God, and the need to repent that set him free. Mark 1:15 urges us to “Repent, and believe the Gospel.” In Luke 13:5 the consequences of not repenting are stressed “But unless you repent, you will all likewise perish.” Jesus commands it in Matthew 4:17 “From that time Jesus began to preach and to say, ‘Repent, for the kingdom of Heaven is at hand.’”
Thus we have salvation instantaneously as we are justified by what Jesus did and then simultaneously we come into a state of regeneration-cum-renovation as progressively we are changed in an ongoing process (1Corinthians 3: 2-1) of sanctification by the Holy Spirit and the Word of God.