Loyalty is a theme in both works.
Should Nick choose to be loyal to Daisy? Should he be loyal to Gatsby? The question of loyalty is not simple, in the end, as Nick ends up with some secrets that compromise his morals - to some extent. He knows things that could hurt people. He is forced to decide what secrets to keep and this part of the dilemma of his loyalty.
Hamlet has to decide between his mother and father. To kill his uncle, he is, in a way, choosing to remain loyal only to his dead father, rendering his mother a widow twice-over. This is a large part of Hamlet's conflict.
I think you could write a great paper about the idea of self-actualization. For Hamlet, you would focus on how he feels about he task of avenging his father's death and trace how he comes to his final actions and his attitude about those actions. In Gatsby you could trace Gatsby's childhood ambitions as revealed at the end of the novel, as well as the ambitions inspired by his desire to win Daisy. Do these characters ever reach a sense of personal fulfillment? Do they die before that happens? What are they realizing about their lives before their untimely deaths?
Ambition, Greed, Social Climbing, Unrequited Love are just a few more. Good Luck!
I think you could argue that another theme is that we are trapped by the circumstances of our birth. Hamlet was born into royalty. That is what caused his problems. Gatsby was born poor, and wanted to be rich. Neither one could overcome his birth.