I doubt that one essay kept you out – sheer numbers/demographics/small number of spaces for unhooked applicants probably would have done you in regardless of that essay… If the college you took a gap year from has no restrictions on applying to other schools, then go ahead. But I’d assume your school you were already accepted to is still your most likely destination. Also, Harvard is reputed to keep old apps for 3 years, so they can refer back if someone reapplies. Your old essay (and any other comments from their previous admissions decision) will still be there. So if your app was flawed in some way (which it may or may not have been), they will still have that original info.
Personally, I wouldn’t take a gap year for this reason. Harvard is not “required” for anyone to succeed in life. If you’ve got what it takes, you don’t need Harvard.