How can I seek removed from the new owner if the house next door already has an easement?

You will need to look at the documents to see how the easement arose and what it covers. I would suggest engaging an attorney.

If you purchased the house with a driveway easement already over it. It might be a done deal. although you might have a lawsuit against the old owners or the title company who insured your title. However, pay a few $$ and have an attorney review all of the documents because without seeing the documents there is no way I can tell for sure.

I need to more details, and probably look at the recorded easement. If the easement was recorded before you bought the home, your remedies would be against the seller or title company if the easement was not made known to you. If it was fraudulently recorded after you had bought the home, you could get a court order to remove it.