Welcome to Cruisemates!
Unfortunately, NCL doesn't offer self service laundromats
. At some point during your cruise (about halfway, usually) there will be a laundry special for "all you can fit in the bag" for about $15.00-20.00.
Roll your clothes and "squish" out all the air and you can get quite a bit into those laundry bags!
You can also send clothes to be pressed for a very reasonable price.
Have a great cruise!