Since the events in "The Great Gatsby" take place over the course of six months, many gaps in action occur. In fact we readers often are not told of many events that took place over the summer of 1922. We also do not know much about what happened in the relationship of Tom and Daisy, and Daisy and Gatsby, prior to the summer of 1922. If you could write a chapter in The Great Gatsby, what would happen? When would it happen? What would the characters in the novel say?
I would write a chapter that delves into Gatsby's criminal activities with Wolfsheim. Much is implied in this regard (bootlegging and bond theft), but very few facts are provided. How did Gatsby actually acquire so much money in such a short period of time? Did he "manage" others, acting as Wolfsheim's front man with groups like the American Legion, or did he participate in specific criminal acts? Had Gatsby actually killed anyone during his "work" with Wolfsheim? Quite an interesting portrait of the criminal activity rampant in the Roaring Twenties could be developed in such a chapter. These details could come to us from Gatsby through Nick. Wolfsheim certainly wouldn't tell Nick anything about his "business," but by the end of the novel when his defenses are down, Gatsby shares everything with Nick.
I think that I would probably write a chapter on that shows the couples in their more private moments, which would serve to show why the characters are dissatisfied in their marriages--perhaps one that showed an interaction between Tom and Myrtle or Daisy and Tom. Gatsby provides some details about these couples, but the conclusions that we draw about these 4 people and their marriages are based off of very little information (which is actually one reason why I love the book!). This would be difficult because Nick, as the narrator, would have to be present during these moments--Nick's character, from what we know, would do his best to avoid these situations, rendering this chapter nearly impossible to write! It would be interesting to read though if one could pull it off!