If you live on a high floor of a building that has an elevator available, then yes, you should reserve it for the movers unloading your items. You’ll need to call the concierge to make the reservation before you book the movers. You should be able to reserve the elevator for a 3-4 hour window of time. The apartment may hang protective blankets in the elevator to prevent scratches or other damages. There’s no charge associated with an elevator reservation.