Clandestine cargo missions will come available at level 9 and are only available at airports without a tower (purple ones on the map). If there are none available, try shutting the game down and restarting it as this will reset the jobs. Unlike other cargo missions, Clandestine ones require you to keep the aircraft below 1,000ft above the ground. Therefore, it is recommended that instead of traveling over islands, you travel round the coast of them. Even though this will take longer, it will also mean you can keep an accurate eye on you height by staying below 1,000ft. It also means you are unlikely to stray above it accidentally as there will be no valleys beneath you which can rapidly increase your height off the ground. You will also occasionally need to stay clear of other aircraft.
Also note that unlike other cargo missions, you can not skip ahead in these so make sure you have the time to complete the flight. If you can get the plane to stay level when traveling across water, you can leave it flying for a bit and come back later.
You have to deliver 4 tons in total or 3628kg. It is recommended that you try to find a mission delivering 800kg or more in less than 50nm. Also once you have completed a mission, you can chose play again and replay the mission rather than having to find another one.