It’s not possible to extend a booking once it has started. If you’ve booked a car park where a driver is arranged for you, such as meet and greet, just give them a ring so they know when you're expected - their contact details are on your confirmation.
Otherwise, collect your car as normal and then pay for the additional time when you exit the car park. You’ll be charged at their standard rates, at their discretion. If the additional time is due to a flight delay keep the receipts for the overstay charges to claim back on your travel insurance.