When Citigroup Inc. went searching for a new deputy general counsel, it didn’t have to go very far. It promoted one of its own: Kevin Thurm.

He may be an attorney with a degree from Harvard Law School, but Thurm, 48, has spent most of his career in administrative and government posts. And that’s invaluable experience for financial companies like Citigroup as they grapple with new rules and regulations for everything from executive pay to corporate governance.