Hi Jane,
It is hard for me to comment further without seeing the easement agreement, and the plan which shows the easement, and indicates the old and new driveways you have mentioned.
From what you have described the new driveway is on your land, and the old driveway is on your neighbour's land.
As your new driveway did not exist at the time the easement agreement was reached... I would tend to think that the easement would have been established to operate together with the old driveway... and creating a new driveway would not alter your legal rights with regards to the old driveway...
However, I am speculating without seeing the facts.
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Kind regards