(transitive) to remove a car or other vehicle from a parked position
1950, The Deseret News, vol. 332, no. 33, "Mother Recovers Car Outbound Son Parked:Tuesday Mrs. Jennie Anderson, 366 North Ninth West St., received the ten-day-old letter asking her to go to Seattle and unpark the car.
(intransitive) to remove a car or other vehicle from a parked position
1969, United States Court of Appeals District of Columbia Circuit, 409 F.2d 1130:A small portion of that area near the sentry booth was left open for vehicular movements essential to parking and unparking.