It is often noted that Captain Hook operated under the tutelage of Captain Jack Sparrow, I'm sure you have heard of him. Sparrow often being the tricky man that he was, had managed to obtain an illicit and false Letter of Marque from his time in Tortuga, before being marooned by Barbossa.

It's often believed that Hook, the only known escapee from the Black Pearl's capture by Commodore Norrington, took with him some of the collection of illicit documents. When the British East India Company under Lord Beckett began the crackdown on piracy in the Caribbean, Fontleroy Smee-Gibbs, half brother of Joshamee Gibbs of Sparrow's crew, sent word for them to flee the area.

Unfortunately, during Hook's time hiding at Wapping Docks in London, he lost his hand which held the portfolio of documents when an alligator (not a crocodile as is widely believed), meant for King George's zoo at the Tower of London, escaped during a pickpocketing attempt by a young street urchin only known as Pan, who is believed to be have been part of the notorious Fagin's crew of street theives. (Fun fact, George "Brick Top" Fagin, the famous unlicensed boxing promoter, dog fighter, and crime boss was a descendant of Fagin). Coincidentally, this was caused by Sparrow's rather destructive escape from the Admiralty Court.

After loosing his hand, Hook, never a very stable man, used his contacts with famed privateers Captain's Blood, and Sir Henry Morgan, to get in contact with the Dread Pirate Roberts to secure a ship from Captain Vallo under false pretenses. After securing his ship, he manipulated Prince Humperdinck to get him in contact with a Miracle Worker only known as Max, who supplied him with a map that could help him locate this Pan boy, who had fled the city. After securing the map, he recieved a letter of Marque and Especially Reprisal against The Dread Pirate Roberts again under false pretenses to pursue Pan as well as notorious tax evader Yellowbeard.

After sailing from Florin, Hook ran into an old foe by the name of William Hossenphepper, off the coast of Sumatra. The two traded shots and boarded each other. During the fight, Willy lost his eye, leading to his moniker of "One Eyed Willy". However, Willy did manage to escape with the falsely obtained Letter of Marque. Later, Humperdinck discovered Hook's treachery, and in order to obscure that he had been taken advantage of again, pursed Willy, who disappeared under mysterious circumstances off the coast of what is now Oregon.

By the time Hook had tracked down Pan, his Letter of Marque and Especially Reprisal, was considered null and void under Florin and Gilder law.

Sources:

On Stranger Tides by Tim Powers

A Right Mess of Things: Florin Geo-Politics in the Humperdinck Era by Wesley Farmer

Re-Evaluating the Influence of London Street Crime by Wayne Blackadder

The Sparrow Flew the Coop: The Greatest Pirate of All Time by Captain Carl. USN. Ret.

Captain Hook was not a real guy. He is a fictional character from (originally) J.M. Barrie's Peter Pan, a play (1904) and later a book (1911).

EDIT: Maybe the question is whether there's any fictional lore in the "Peter-Paniverse" of Hook being a privateer for the British Crown as opposed to a simple robber on the high seas, but it's not really possible. British privateering was abolished in 1856 by the Paris Declaration Respecting Maritime Law, so it wouldn't be possible for Hook to be authorized by the Crown in the early 1900s. But Hook himself is anachronistic - he dresses like a man from the 18th century (frockcoat, long curls, etc.) - so maybe the same rules of time and space don't apply in Neverland.

Barrie never mentioned Hook being a privateer, although he did give some other interesting background on the character.