What you want is confirmation of receipt of the essay.
This is not only ugly, it is potentially confusing, because a receipt is a confirmation of receipt of the essay; and we call that a receipt for the essay.
This is what happens when people use nominalized verbs instead of actual verbs. Your instinct to turn those nominals back into the verbs they come from is commendable. Do so at every opportunity.
After you have reviewed the essay, please confirm that you received it.
Three verbs, no nominals, no prepositions.
I can't think of any English term that is regularly used for this – at least, not in a noun form.
As Steve Ives mentioned in his answer, this is how I would ask the question:
What time are you leaving?
The term departure time is grammatically correct, but that expression is normally reserved for transportation: planes, trains, and busses. And it generally refers to the time that the conveyance departs (everyone knows that passengers must arrive earlier than that so they can all board before departure.)
If you want to tell your friends that you'll be leaving the campus at 5 o'clock, you'd say something like:
I should be leaving the campus around five.
or:
I should be done at the campus around five.
You'd only use departure time if you were trying to be funny by making something ordinary (i.e., leaving the campus) sound very official:
My departure time from campus will be 5 o'clock.
I could say a father saying this to his young children, if they were leaving for a trip the next day:
Our departure time will be 8 AM.
but that would be overly formal and therefore deliberately humorous. A more natural way to say it would be:
I want us to get out of here by eight.
or:
Let's be pulling out of the driveway before 8 AM.
The same holds for arrival time. We typically say something like:
We should be there a little before 10.
not:
We have a 9:55 estimated arrival time.
unless we are trying to be somewhat humorous by being overly technical.
Best Answer
The pronoun there can play the role of a subject of to-infinitive clause, just like any other pronoun, e.g me, you etc
In all the sentences above, the bolded words are the subject of the to-infinitive constructions.
In view of that, your sentence is correct. But in reality such construction of for there to be is more common in speech than in written text.