To be eligible for new elite ship designs you need the first design, named "Terror of the Sea". This design can be bought at the market cove.
New elite designs are awarded when you have recieved enough elite points. Each elite cannonball counts as one elite point, while elite healingballs counts as two elite points. During special events, you may get x2 elite points from cannonballs and x3 from healingballs.
View the Elite Designs