Luffy first uses Supreme King Haki (Conqueror's Haki) visibly in Episode 516 (anime) during the Dressrosa arc against Doflamingo's subordinates and later shows a stronger application in Episode 868 (anime) during the Wano/Onigashima events against Kaido's forces.
Water 7 Arc (Episode 280-281) hinted but clearly not on full display.
We will test each definition against the anime episodes. which episode luffy use supreme haki
During the battle against Doflamingo
In the vast and vibrant world of One Piece, the concept of Haki has become an integral part of the narrative. This spiritual energy, also known as "will" or "spiritual power," allows users to sense the presence of others, predict their movements, and even imbue their physical bodies with a powerful aura. Among the three types of Haki, Conqueror's Haki, also known as Supreme Haki, is the rarest and most formidable. It is this type of Haki that has garnered significant attention from fans worldwide, particularly when it comes to Monkey D. Luffy, the main protagonist of the series. Luffy first uses Supreme King Haki (Conqueror's Haki)
If you want to see Luffy use the Advanced form of Supreme Haki (coating his fists without touching the enemy), the specific episode is:
Analysis: Implications and Impact
Episode 852: His intense mental battle and Haki clash against Charlotte Katakuri. ⚡ The Advanced Stage: Infusion