I was interested in this too and looked to see what my local uni library had in the stacks. I found some interesting material from the conclusion of James Davey's In Nelson's Wake: The Navy and the Napoleonic Wars published by Yale in 2015.

In the conclusion, Davey notes that between 1815 and WW1, the empire added 10 million square miles of real estate. The maritime fleets had to navigate through those new waters and coasts, but the naval forces were reduced significantly. In the aftermath of Waterloo, the navy was ordered to reduce the fleet to 12,000 seamen, 5,000 marines and maintain only 12 ships-of-the-line. Most junior officers left the navy to join the maritime fleets or foreign navies while others kept their commissions to live on halfpay. I'll quote a telling line from pg. 319: "The navy went from being the nation's most meritocratic profession to a bastion of privilege and elitism in the Victorian age."

From his notes, I would suggest looking at Kennedy's The Rise and Fall of British Naval Mastery and Parsons' The British Imperial Century.

So if you were a young lieutenant without political allies in Parliament, the Admiralty, or Court, you would probably find a decent gig in the maritime fleets. South American states were looking to build their fleets by the 1820s so a savvy naval officer might have looked into that world as well.