The first book in the series is Lord John and the Private Matter. The main character is Lord John Grey, an important but not always present character in the Outlander books. Goodreads has this summary of the plot:
The year is 1757. On a clear morning in mid-June, Lord John Grey emerges from London’s Beefsteak Club, his mind in turmoil. A nobleman and a high-ranking officer in His Majesty’s Army, Grey has just witnessed something shocking. But his efforts to avoid a scandal that might destroy his family are interrupted by something still more urgent: the Crown appoints him to investigate the brutal murder of a comrade in arms, who may have been a traitor.And lest you think that I am just feeling too lazy with my summer brain to actually write my own summary, I will tell you that I've spent the last 20 minutes composing and erasing prospective summaries-the plot is intricate and detailed, with many moving parts. Gabaldon's Lord John reminds me of the William Monk books by Anne Perry, who also writes very well-researched historical mysteries. But there is one major difference-Lord John Grey is gay. Since the 18th century was not known for its acceptance of homosexuals, this adds tension to the whole story. Gabaldon gives us a fascinating look at the gay culture of London in the mid-1700s, and weaves it seamlessly into the story so that it feels authentic rather than contrived. Because Lord John is also a character from the Outlander series there are a few mentions of Jamie Fraser and Claire, but for the most part this is a stand-alone series that does not require that you read the very loooonnnnngggg Outlander books to enjoy. In fact, if you enjoy Gabaldon's writing but think the Outlander books are too long, then this series is for you!
Obliged to pursue two inquiries at once, Major Grey finds himself ensnared in a web of treachery and betrayal that touches every stratum of English society — and threatens all he holds dear. From the bawdy houses of London’s night-world to the stately drawing rooms of the nobility, and from the blood of a murdered corpse to the thundering seas ruled by the majestic fleet of the East India Company, Lord John pursues the elusive trails of a vanishing footman and a woman in green velvet, who may hold the key to everything — or nothing.