Hedge fund investor Elliott Management Corp. is once again seeking to shake up Duke Energy, publicly questioning whether the North Carolina-based utility’s current leadership should continue to manage its businesses outside of the core Carolinas footprint.

In a letter sent to Duke’s board of directors, Elliott acknowledged that fellow investors, stakeholders, market analysts and advisors believe that “Duke owns one of the highest-quality collections of premium utility businesses propelled by tailwinds from constructive regulation, positive demographic trends and significant investment opportunities.” However, there is significant room for improvement when it comes to operational execution and attaining a premium valuation for the company, it said.

Elliott called on Duke...