The Holy Spirit will come in a new way. He will come to glorify Jesus. And when he comes, he will convict (or convince) believers that the world completely misunderstands sin, righteousness and judgement.
Martin Luther said that Jesus went on to give definitions of those three words that are radically different from what the world thinks they mean.
The world thinks of sin (if it believes in it at all) as “breaking the rules,” violating the commandments, doing bad things. But in Jesus’s death on the cross, all of those sins are forgiven. The one that remains is the refusal to accept his gift of forgiveness and believe in him.
The world thinks that righteousness is the opposite of sin - keeping the rules and doing good things. Jesus said that our righteousness - our right standing before God - is not a matter of what we have done at all; it is a matter of what he has done on our behalf!
Jesus completed his work here on earth and went to the Father on our behalf. Our righteousness is his finished work.
(If trust in his finished work is our righteousness, sin is our refusal to believe and trust in that finished work.)
The world thinks that judgment is what happens to bad people. Jesus said that judgment happens to the ruler of this world, and it need not fall on anyone else. That is good news! The Holy Spirit glorifies Jesus by convincing people that such good news is true.Commentary on John 16:7-11, from “Anointed by the Spirit.”