Who else approaches Dimmesdale just as he invites Pearl and Hester to join him on the scaffold?Nathaniel Hawthorne's The Scarlet Letter
This scene from The Scarlet Letter is the very climax of the novel. For, it is the point at which the character, Arthur Dimmesdale, resolves the terrible conflicts of conscience and soul in which he has been engaged since the first scaffold scene. By standing upon the scaffold and confessing his sin, spiritually Dimmesdale is released--the truth does, indeed, set him free. For, Dimmesdale is set free from the devilish torture of the fiend that Roger Chillingworth has become. Standing beneath the minister, about whom he told Hester in Chapter IV, "Sooner or later, he must needs be mine," now has lost the victim whom he has tortured in his desire for vengeance.
Having attempted to deter the minister, to "snatch back his victim," he has promised Dimmesdale that he can yet save him:
"Madman, hold! What is your purpose?...Wave back that woman! Cast off this child. All shall be well! Do not blacken your fame, and perish in dishonour! I can yet save you! Would you bring infamy on your sacred profession?"
Responding much as Jesus did when the Satan tempted Him [Matthew 4:1-3] in the desert, Dimmesdale tells the dark and evil man,
"Ha, tempter! Methinks thou art too late!...Thy power is not what it was! With God's help, I shall escape thee now!"
In his confession to the town, Dimmesdale is freed from his secret sin; he fulfills the theme of Hawthorne that is stated in the concluding chapter:
"Be true! Be true! Show freely to the world, if not your worst, yet some trait whereby the worst may be inferred!"
For, by being "true," no one can be false to any other.
I assume that you are asking about what happens in Chapter 23. If that is the case, the answer is that it is Roger Chillingworth who approaches Rev. Dimmesdale after he has invited Hester Prynne and her daughter (their daughter) Pearl to join him.
This is significant because of what Chillingworth has been doing in the rest of the book. He had been Hester's husband and he hates Dimmesdale. Because of that, he has been sort of torturing Dimmesdale psychologically. He wants to keep doing that and so he does not want Dimmesdale to admit that he is Pearl's father.
So Chillingworth approaches to try to keep Dimmesdale from confessing so that he (Chillingworth) can keep holding the secret over Dimmesdale's head.