Our salvation is based on what we believe, not on how we behave. In the gospel of John alone we can find numerous confirmations of that. John 1:12-13, John 3:16, John 5:24, John 6:28-29, John 6:40 are examples.
The Greek word translated “repent” means to change your mind about something. When people change their mind and begin to believe they are sinners in need of a savior, and that Jesus died for their sin and rose again, they have repented.
In Ezekiel 36:26 God promised to give Israel a new heart, but this will happen after the 2nd Coming. There is no place in the New Testament that says we receive a new heart upon believing. It says because of our faith God considers us to be a new creation. We will get a new heart at the rapture but until then still have our old heart with its sin nature.
Every believer sins and every sin we commit grieves the Holy Spirit who is sealed within us for the day of redemption (Ephes. 4:30).
As born again believers we have God’s Spirit in our heart (2 Cor. 1:21-22) guiding us in ways that are more pleasing to Him. On the whole, our behavior will change for the better because of this. But these changes can take place at different times and in different ways for different believers. How they do is between each individual and the Lord and is no one else’s concern.