Part of the mastery of Browning's art in this poem is that we are only told who the audience of the Duke's dramatic monologue is at the end of the poem, after he has seemingly quite cheerfully narrated how he had his "last Duchess" disposed off because of how, in his perception, she bestowed attention of others. Thus, having established the immense pride and cruelty of the Duke, it is highly ironic that we discover in the last few lines that the silent listener is a representative from a Count whose Duke the daughter is negotiating to marry:
The Count your master's known munificience
Is ample warrant that no just pretense
Of mine for dowry will be disallowed;
Though his fair daughter's self, as I avowed
As starting, is my object.
Now, when we think about this, this is either incredibly ironic or/and it is incredibly chilling. Either we think that the Duke has no awareness of what the story of his last Duchess is doing to the listener, or, he is deliberately sending a message to the Count about the kind of behaviour he expects from a wife and the kind of response he can expect if his daughter does not behave accordingly.