You get experience for each ship you sink/board at sea (unique ships will give you a Triumph), as well as for some events and your rank rises. You can check your current rank in “Ship Management” screen – it’s expressed in stars under your character portrait, from 1 to 5.
You can also easily do this if you have at least 4 Berath's Blessings. Just start a new game and spend those 4 blessings on “Experienced Ship Captain” – you will begin the game as an Expert ship captain.