This book could easily provide material for long papers and short ones, but, in order to do the subject justice, and since this is such an expansive book, it is necessary for a short essay to choose a relatively compact and limited topic. For example, choosing to discuss the significance of the title, which pervades every story and almost every situation in the novel, would be unsuitable for a short essay. Likewise, any subject or theme that covers both the time periods (1980s London/British Museum/Roland and Maud, and the past, Christabel and Randolph) would probably be too big for a short essay. It would probably be more manageable to choose an idea or theme from one of the time periods, as a discussion of the theme from both time periods might prove to be too lengthy.
Another choice would be to choose a discussion of a secondary character (such as Beatrice Nest, starting about at Chapter 7) and his or her importance to the story. Would Maud and Roland ever have been able to solve the mystery of the letters if it hadn't been for Beatrice's ignominious research of Randolph's wife's journal? This kind of question could be easily dealt with in a short essay.
It would be possible, perhaps, to discuss the Melusina poetry fragments as an effective, short essay. Christabel, the "fairy poet", is obscure and hard to understand. An interesting discussion of that Melusina meant to her is in Chapter 28. To discuss Christabel as a poet, in her time and situation, and what the fragments of her (invented) poetry (written, of course, by the author A.S. Byatt) reveal would be an interesting short essay. It could be expanded into a longer paper later, if one is required for the class. But the inclusion of invented, intended-to-be-Victorian poetry written expressly for the purpose of a novel is an interesting subject in itself. Do you "buy" the poetry as "Victorian" enough? Did it distract you or bring you closer into the novel?
Another, entirely different essay could be about the Roland/Blackadder relationship. How does modern academia actually stifle rather than encourage scholarship? Is this kind of competition good for the refinement of the young scholars, or is it detrimental? This is discussed in Chapters 1-3, and in various other places in the novel.
This is such a big book, with so many interesting characters, themes, and situations. Choose what interests you: do you like a character, perhaps, such as Lenora Stern or Mortimer Cropper, the two American scholars in the novel? Do you think that these characters are well-drawn and meaningful to the plot? Did you enjoy the poetry of Ash and LaMotte? Choose an aspect of the book -- be it a character, a theme, or an idea, and focus on it, limiting it to a workable size so that it works effectively in a short format. Good luck!
One possibility for a short essay on Possession would be to explore the emotional impact on the reader of Byatt's juxtaposition of Victorian literary devices with modern literary devices as she tells the two unrelated stories. For instance, does the inclusion of letters and journals in the Victorian story, told with the occasional aid of an omniscient third person narrator, increase the emotional response evoked by the modern adventure story? Or do the two approaches evoke separate qualities of emotionality? Or do the two approaches evoke complementary emotions (pity and sorrow) or opposing emotions (anger and love)?
Whichever is true of the emotions evoked, do the emotions serve to further Byatt's overall thesis, her themes, her symbolism? Or do they each take the reader down their own thematic and symbolic paths? You might conclude with asking what purpose Byatt may have had in her choices related to approach and emotions and whether her device was effective.