Terry Benedict (Andy García) locates all eleven members of Danny Ocean's (George Clooney) gang, demanding they return the $160 million they stole from his casinos plus $38 million interest. Short by half, the group schemes to stage another heist in Europe to avoid problems with United States authorities. They are tipped off by an informant named Matsui (Robbie Coltrane) about the location of the first stock certificate ever. After a complex series of schemes they find the document has already been stolen by "The Night Fox", another master thief. Europol Detective Isabel Lahiri (Catherine Zeta-Jones) is called in to investigate the theft and realizes that her talking earlier about a particular burglary with Rusty (Brad Pitt) during their relationship, would have given Rusty the idea of how to solve the complication the gang would have come up against. Surprising the group at their accommodation, she warns them they cannot beat the Night Fox or his mentor, the mysterious master-thief "LeMarc", both of whom excel in practicing the "long-con". She has been hunting both for years.
Danny and his gang discover the Night Fox is Baron François Toulour (Vincent Cassel), a wealthy businessman who has a mansion on Lake Como. Toulour invites Danny to his mansion and reveals that he had hired Matsui to inform the gang about the certificate in order to arrange the meeting with Danny. Toulour is upset that LeMarc did not describe him as the best thief in the world, and challenges Danny to steal the Fabergé Imperial Coronation Egg. If Danny and his gang win, Toulour will pay off the debt to Benedict.
Danny and his gang begin to plan an elaborate heist to swap the egg for a holographic recreation, but the engineer hired by the group accidentally tips off Lahiri to their presence, and she captures most of the gang on their first attempt. Linus (Matt Damon) comes up with a second plan involving Danny's wife Tess (Julia Roberts) posing as a pregnant Julia Roberts in order to get close to the Egg and swap it. They are foiled by Lahiri, and the rest of the group are captured. Lahiri is told that they are to be extradited to the United States. Linus is chosen first to be interrogated by the FBI agent (Cherry Jones) assigned to collect them. It turns out that she is his mother, who organises the release of the whole gang. She points out to Lahiri that she will face only retribution for her forging a signature on a Europol form to obtain the necessary arrest warrants for Ocean's gang.
Some time later, Danny and Tess return to Toulour's estate where he reveals his glee at their failure. Toulour claims to have stolen the egg at night using his agility and Capoeira skills to evade the heavy security. Toulour's celebration is short-lived when Danny reveals that his group stole the egg while it was in transit to the museum and Toulour realizes they were tipped off by LeMarc. A flashback reveals that Danny and Rusty had met LeMarc earlier when he revealed his confidence trick intended to humiliate Toulour, and at the same time, to restore to himself the Fabergé egg that he had stolen years ago and had returned following his wife's wishes. Toulour is forced to admit Danny won the bet and gives him the money for the debt. They pay back Benedict and promise not to perform any more heists in his casinos—even as Toulour himself is in the background spying on Benedict. Rusty takes Lahiri to a safe house that he claims has been lent to him by LeMarc. She is reunited with her father, who is revealed to be the man she has been pursuing for years: LeMarc (Albert Finney). The final scenes of the film, in which the primary characters enjoy a private poker session, imply that she and Rusty have re-kindled their relationship.

Question: What does "The Night Fox" promise Danny if he gets the Coronation Egg?
Answer: That he will pay off Danny's debt to Terry
Alternative answer: to pay Danny's debt off to Benedict.