Zelda and Dark Link have not been seen interacting much as Dark Zelink is considered to be a crack pairing. In the Adventure of Link, Dark Link is the final obstacle that Link must face in order to wake up Princess Zelda.
Dark Zelink has a small amount of popularity in the Zelda fandom. It is considered a crack pairing and is mostly shipped for the "opposites attract" factor. Since Dark Link is a doppelganger or another version of Link, some fans theorize that Dark Link would have the same feelings that Link has, including possible feelings for Princess Zelda.