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Ledge-Trumping is the technique used to force the opponent off the ledge right as they reach it after their recovery. Ledge-Trumping was introduced in Super Smash Bros. for Nintendo 3DS and Wii U and continued in Super Smash Bros. Ultimate, it replaced Edge-hogging from Super Smash Bros. Brawl essentially, as Edge-hogging doesn't work in any later title. Ledge-Trumping forces the player that just grabbed the ledge to be thrown off, making them vulnerable to aerial attacks, specifically Back Air in most cases.
To do a Ledge-Trump, you have to catch the ledge just as the opponent does so (or slightly later). To do this in Ultimate you dash to the edge of the stage and when you're about to fall off, you press down on the left-stick, then immediately press into the direction of the stage with the left-stick. You can also turn around jump off and grab the ledge, similar to a Reverse Aerial Rush (RAR), this is the only way to do it in Smash 4.