reservations-only system; by-appointment-only system
Used for businesses, services, or events that require advance booking and do not accept walk-ins.
This restaurant operates on a reservations-only basis.
Because it is by appointment only, we do not accept same-day visits.
予約制 means a reservation system in general, while 完全予約制 emphasizes that reservations are strictly required with no exceptions.
Compound of 完全 (complete) + 予約 (reservation) + 制 (system).