When Citigroup’s biggest shareholder, Prince al-Waleed bin-Talal, wanted an introduction to new CEO Michael Corbat, the Saudi billionaire turned to Alberto Verme. Al-Waleed is one of a glittering roster of clients assigned to Verme, Citi’s chairman of banking for Europe, the Middle East and Africa. The London-based deal maker has built his career on his relationships with the powerful. Last year Verme logged 250,000 miles and attended more than 240 meetings with top executives. “I like to be as close to my clients as possible when they need me,” says the 55-year-old banker.

Verme spent much of the past summer advising Igor Sechin, president of Russia’s Rosneft, on the state-owned oil giant’s $55 billion acquisition of TNK-BP from U.K. oil company BP and Russia’s AAR Consortium, a venture of Alfa Group, Access Industries and Renova Group. The long-simmering deal will boost Citi’s EMEA M&A business when it closes in....