Tim Throsby is Barclays’s new corporate-and-investment-banking boss. A relatively unknown former JPMorgan Chase executive, Throsby was recruited by Barclays CEO Jes Staley to run Barclays International - which accounts for more than 2/3’s of the bank’s revenue. The 50-year-old Australian spent most of his career overseeing equities-trading desks.

Now he is responsible for a franchise that includes German credit cards, rich clients in Switzerland and a bond-trading desk in New York.

How Mr. Throsby fares will help determine whether Barclays can thrive as one of the U.K.’s last diversified universal banks. It will also test Mr. Staley’s decision to populate Barclays’s senior ranks with executives from his former employer, JPMorgan. That includes Barclays’s new CFO, CRO, and COO – all of whom are alumni of the U.S. bank.

Barclays has no immediate plans to pump more capital into Mr. Throsby’s unit, according to a person familiar with the matter. However, the executive will have freedom to reallocate resources to the investment bank from within his wider business, which includes big corporate customers, a U.S. credit-card business and wealth management, this person said.

In 2016, Mr. Staley unveiled a sweeping restructuring of Barclays, which included paring its hundred-year-long presence in Africa in favor of a contrarian bet to stick with its unloved investment bank. Shares have rallied 50% over the last 12 months, helped by the prospect of rising rates.

“The key question is whether Barclays is benefiting from a rising tide or whether the action he is taking is a dominant driver,” said Thomas Moore, an investment director at Standard Life Investments, which owns shares in the bank.

WHO IS TIM THROSBY.    Known for his tieless appearance, Mr. Throsby built a reputation as a decisive, and at times abrasive, operator over a 3-decade career. At J.P. Morgan, he overhauled the equities franchise, competing fiercely to access the bank’s huge balance sheet and allow clients to take more risk. Former colleagues and clients expect the rugby-loving executive to repeat the feat at Barclays’s investment bank.

Mr. Throsby forged his career in Asia jumping between big investment banks. After stints at Macquarie Group, Goldman Sachs and Lehman Brothers, he moved to Citadel in Hong Kong. When the hedge-fund firm retreated from Asia in the throes of the financial crisis, Mr. Throsby quit and traveled to the U.K. to study law at Oxford University. He never finished. In 2010, he joined JPMorgan to run its European equity derivatives business. It was there Mr. Throsby caught the eye of Mr. Staley, who was heading up the lender’s investment bank at the time.

By 2012 Mr. Throsby was in charge of JPMorgan’s lagging equities division. He helped overhaul electronic trading and attract more hedge-fund business. He pushed to bring more capital to the equities division and to allow clients to take more risks. At times, he butted heads with other managers at the bank by encroaching on their territory, people who know him say, such as by helping clients trade in regions overseen by other managers.

Between 2012 and 2016, JPMorgan’s equity-markets income rose 30% to $5.74 billion, in part fueled by its equity-derivatives business.

Mr. Throsby, who has 6 children, also found time to buy and renovate his old family home, Throsby Park, an Australian colonial-era estate.