The phrase "carp leaping the dragon gate" (鲤鱼跃龙门, lǐyú yuè lóngmén) is a very old Chinese idiom and mythological reference.
It comes from a legend about the Yellow River:
There is a place on the river called the Dragon Gate (龙门, Lóngmén), where the current is extremely fast and turbulent. It was said that if a carp could leap over this gate, it would transform into a dragon. Since carp are ordinary fish and dragons are exalted, the story became a metaphor for someone overcoming incredible challenges to achieve greatness.
Symbolism
Exams & Success: In imperial times, it was especially used for scholars passing the imperial examination system (科举, kējǔ). Passing meant a leap in status, like a carp turning into a dragon.
General Achievement: Today, it's used more broadly for achieving a breakthrough against great odds — promotions, academic success, or any life-changing accomplishment.
So when a character says something like "this is my chance to leap the dragon gate," they're saying:
"This is my opportunity to transform my fate and rise above ordinary people by seizing a rare chance."
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I pluck this from The Cube Queen's Apocalypse Feast, Volume 3: A Torrential Banquet, Chapter: Vice President Jing Shu's Assessment Begins