This is a really good question, and it demonstrates your interest in writing the most effective essay possible; so I commend you for asking. The short answer is that it depends on the type of essay you will be writing. The general rule for all essays--and any other type of writing--is to pick a tense and stay consistent. Shifting verb tenses is one of the most distracting things for a reader to endure; write in one tense and change tenses only to indicate a shift in time or some dramatic purpose.
Narrative essays are a bit of an exception to the rule because they tell a story, and the nature of storytelling is to shift sometimes between the past, present, and future. Again the key to this is to start in one tense and use it consistently until you have a reason to shift in time.
The Purdue Online Writing Lab is an excellent tool for all kinds of grammar and writing issues, and these are their exact recommendations:
- Rely on past tense to narrate events and to refer to an author or an author's ideas as historical entities (biographical information about a historical figure or narration of developments in an author's ideas over time).
- Use present tense to state facts, to refer to perpetual or habitual actions, and to discuss your own ideas or those expressed by an author in a particular work. Also use present tense to describe action in a literary work, movie, or other fictional narrative. Occasionally, for dramatic effect, you may wish to narrate an event in present tense as though it were happening now. If you do, use present tense consistently throughout the narrative, making shifts only where appropriate.
- Future action may be expressed in a variety of ways, including the use of will, shall, is going to, are about to, tomorrow and other adverbs of time, and a wide range of contextual cues.
For most descriptive, argumentative, and expository (informative) essays (which covers nearly every possibility), use present tense throughout, changing only when it is appropriate for effect or to enhance meaning. Happy writing!
If your essay is analytical (and I'm struggling to think of any other reason you'd write an essay about The Great Gatsby) then I'd put it in the present tense.
Gatsby loves Daisy, but Daisy is married to Tom. Gatsby doesn't have the bloodline to impress her; all he has is money. So he throws lavish affairs at his ostentatious house in a effort to show her how riche he is, and only comes off looking painfully nouveau.
Even though the book is in past tense, as you read it you are in the book's "present," so you are in the action. When you're analyzing it, you're analyzing what occurs. You'd use past tense if you were talking about something which happened in the character's past:
Jane Eyre is hired by Mr. Rochester as a governness. When he asks her if she can play the piano, she modestly replies, "A little," and proceeds to reel out some Chopin. She learned the piece when she was a child, when she lived at Lowood. Mr. Rochester snorts at how English girls are brought up to downplay their achievements.