A Relentless Rake by Anna Harrington

Notorious rake Alexander Sinclair, Earl of St James, takes pride in displaying his sins. When he’s tasked by the Home Office with finding the men who attempted to assassinate the prime minister, his hunt leads him to Olivia Everett, a most proper schoolmistress who wants nothing to do with a profligate nobleman like him.
Unknown to her, Olivia’s brother Henry has been working with the revolutionary group planning to overthrow the government. Shocked and hoping to save her brother, Olivia agrees to help the persuasive earl. But the closer they get to uncovering the villains, the more Alec and Olivia will need to trust each other.