Zoro uses Conqueror’s Haki against King in One Piece episode 1060 in the anime, with the fight then continuing into episode 1062.

Quick context

The clearest on-screen awakening of that power happens when Zoro realizes he needs to control Enma’s output and then unleashes Conqueror’s Haki during the King fight. Some coverage also links the manga version of the moment to chapter 1033.

Episode notes

  • Episode 1060 : Zoro first visibly taps into Conqueror’s Haki in the anime against King.
  • Episode 1062 : The Zoro vs. King fight concludes.

TL;DR

If you mean the anime moment where Zoro first uses it against King, the answer is episode 1060.