To unlock the full outfit, first you have to complete the Captain of Silvered Water commendation, which you receive for placing in the top three 100 times in The Arena.
After that, just go to any clothing vendor and purchase the four items.
Glorious Sea Dog Hat - 6,800 Gold
Glorious Sea Dog Jacket - 6,750 Gold
Glorious Sea Dog Hook - 4,050 Gold
Glorious Sea Dog Gloves - 1,350 Gold
Total = 18,950 Gold