After Emma is incorrect about Mr. Elton’s feelings for Harriet (as he actually loves Emma instead), she promises to stop playing matchmaker but then continues to do so—an example of dramatic irony. Emma makes it clear to herself and readers that she has learned her lesson about meddling after reflecting on how wrong she was about Mr. Elton and how much she hurt Harriet in the process:
The first error and the worst lay at her door. It was foolish, it was wrong, to take so active a part in bringing any two people together. It was adventuring too far, assuming too much, making light of what ought to be serious, a trick of what ought to be simple. She was quite concerned and ashamed, and resolved to do such things no more.
The dramatic irony comes in when Emma does not stop playing matchmaker, as seen just a couple paragraphs later when she unconsciously begins to consider other suitors for Harriet:
“I am sure I have not an idea of any body else who would be at all desirable for her;—William Cox—Oh! no, I could not endure William Cox—a pert young lawyer.”
Because readers have witnessed Emma promise herself (and also Harriet) that she will no longer meddle, they can appreciate the irony in her immediately going back to her old ways. It hints at how Emma will continue to be trapped by her pride and meddling instincts for much of the book—that it will take more than this moment to make her change her ways.