You don't have to worry about missing the flight if you have a 3 PM flight.
Normally, the ships dock early in the morning and they allow passengers to disembark around 8 AM. If you decide to carry your bags off the ship, you will be the first to disembark. If you have too many bags, get the early dismemberment tags on the last night of the cruise. To make disembarkation easy, NCL uses color coded bag tags which specify the disembark time on it. That way you will be able to disembark after the people who carry their own bags are off the ship. Collect your bags on the port and go through custom and immigration.
In any case, all the passengers will be off the ship by around 10 AM to give the ship staff time to clean the ship for the next cruise.
Number One Contributor
If you have a credit card on file, they will automatically charge your card with any expenditures you charge to your room. On the final night, you will keep all your luggage instead of putting it out to get collected. Once the ship docks and is cleared by customs, you take all your stuff with you and leave. You can actually leave whenever you want once the ship is cleared. By 1030 everyone is usually off the ship no matter what form of checkout you pick.
Top 25 Contributor
Assuming your ship arrives at the pier either 7am or 8am, you should have plenty of time to reach the airport.
Express checkout or the walk off option is where you carry your luggage off the ship yourself, with this option you can leave the ship at any time after the announcement has been made.
Top 10 Contributor
The first group of passengers to disembark are those who "walk off with their luggage". About an hour after they start passengers disembark in groups about every 20-30 minutes depending upon the time slot they have chosen by getting the appropriate disembarkation luggage tags in the Reception area a day or 2 before disembarkation. Usually the ship is cleared of all passengers within 3 hours, so assuming an 8 AM arrival time upon return you should have a 4 hour window to get to the airport and thru security.
Top 10 Contributor