“Having an all encompassing dream sets characters up to fail.” Compare and contrast Fitzgerald’s and Ishiguro’s presentation of the impact of the pursuit of impossible dreams on Gatsby and Kathy in The Great Gatsby and Never Let Me Go respectively.”

Both The Great Gatsby and Never Let Me Go basically show that "having an all-encompassing dream sets characters up to fail," though I think the statement is more relevant to Gatsby than to the characters in Ishiguro's novel.
Jay Gatsby's "all-encompassing dream" is to win the love of Daisy Buchanan, a former lover. She is now married to Tom Buchanan, and he and Daisy are both of "old money," meaning their families have long been wealthy and powerful. Gatsby, on the other hand, did not grow up rich, so he was not able to marry Daisy even though they were in love. As an adult, Gatsby vows to build his wealth and power in an effort to lure Daisy to him. He builds his estate across the water from Tom and Daisy's so that his dream is always in his sight. He develops a reputation for his massive parties, which he nonetheless does not partake in because his only concern is Daisy, and she is not there. Eventually, he and Daisy do rekindle their love, but it ends quickly in tragedy. While Daisy is driving Gatsby's car, she hits and kills Myrtle Wilson. Gatsby is willing to take the fall for Daisy, and Myrtle's husband, George, believing Gatsby was driving the car, shoots and kills him. Gatsby's single-mindedness results in tragedy and pain, not only for himself but also for many around him. Meanwhile, the "old money" characters escape any consequences and are free to continue their reckless lives.
Never Let Me Go is much different in terms of subject matter and tone. Kathy, the narrator, is a student of the mysterious boarding school Hailsham in Ishiguro's dystopian world. She and her friends Tommy and Ruth eventually learn that they were genetically engineered to provide replacement organs for "normal humans." They become "donors," through a series of operations when they reach a certain age. They usually "complete" when they are young adults. Ruth tells Kathy about a rumor that went around the school that couples who are in love can get an exception and have more time to spend together before donating. When Kathy confronts the benefactress of the school, she learns that this was always false. The "all-encompassing" dream they have of being able to live normal lives, or even to have a few more years to spend together, is quickly dashed. Tommy soon completes, and Kathy continues to work as a "carer." Kathy will one day be a donor, as well, and spends her days with those who are in the process of donating and completing. This is certainly a bleak future, and it's tragic, but it's handled in a much less dramatic and certainly less explicitly violent way than what we see in Gatsby.