The grad school I'm applying to accepts extracts from longer essays. I want to send an extract from my strongest (and rather long) essay, but I'm unsure how to go about it. Is it acceptable to take an extract from the middle and send it with a cover note? Or should I keep an introduction and/or conclusion? I'd be grateful for any advice.
I would suggest to focus on the most important part of the essay, i.e. the part you feel the strongest about and where you really get into the details of the topic, and leave out introduction & conclusion for the most part and instead write an abstract which summarises these points. Of course do keep bits of the introduction & conclusion to lead into & out of the topic, but that might only be a sentence or two and mainly for readability.
You don't mention the field. In some fields you might want something that is relatively complete. But in some others, it may be that all that is wanted is a writing sample to show that you can write intelligently. If that is the case, just select something that demonstrates your skill in writing, or argumentation, or whatever is relevant to the field.