I will make the assumption that the recent Luhrmann film is the movie in question. The most elemental condition in which one can see Gatsby trying to recapture the past would be in his desire to love Daisy. Whether one wants to call this trying to woo her over, win her back, or get her to love him, it becomes evident that Gatsby is seeking to recapture the past in his love for Daisy. He wishes to go back to a time in which she was not married to Tom and a time in which he was not so poor when he first saw her. Gatsby's desire to reinvent himself and display the most lavish of parties, as seen in the film, is where he seeks to recapture the past. Consider the description of this in the film:
In the 3-D version, the viewer swoops and swerves through one of Gatsby’s parties in a movement that combines Vincente Minnelli-style suavity with the controlled vertigo of a theme park ride. As it happens, Nick Carraway (Tobey Maguire) compares the sybaritic scene at Gatsby’s mansion to “an amusement park.” And Mr. Luhrmann’s peculiar genius — also the thing that drives cultural purists of various stripes crazy — lies in his eager, calculating mix of refinement and vulgarity.
This construction of reality is where it becomes evident that Gatsby is desperate in seeking to recapture the past. The "amusement park" reality of Gatsby's parties and the "vertigo of a theme park ride" are reflections of a wish to reclaim the past from a brutal present. It is here in which Gatsby is shown in the film as seeking to recapture in the present something that might not have been in the past in the first place. Such a cinematic depiction is where one might be able to see what Fitzgerald described as “a promise that the rock of the world was founded securely on a fairy's wing.”