Arguably, the two most important minor characters are Sibyl Vane and her brother, James Vane. Sibyl, Dorian's first fated love, is of course a very tragic character who is dynamic in the way that she suffers a massive change in her perspective thanks to her relationship with Dorian, that also results in her death thanks to Dorian's lack of regard for her. Note how she describes this central change in her perspective in Chapter 7, after her disastrous performance:
I knew nothing but shadows, and I thought them real. You came--oh, my beautiful love!--and you freed my soul from prison. You taught me what reality really is. Tonight, for the first time in my life, I saw through the hollowness, the sham, the silliness of the empty pageant that I had always played.
Ironically, Sibyl's character moves from art to reality thanks to her love for Dorian, never realising that it is only her art that Dorian loves. Her dynamic character is clearly shown in this crucial change.
James Vane, her brother, is a static character in the way that he does not change significantly during the novel. He is introduced as a brother who is protective of his sister, and his murder attempt of Dorian Gray later on in the novel only supports this. His character does not change essentially in the way that his sister's character does, and as a result he is not a dynamic character.