An activist investor that has long targeted Kohl's is ratcheting up the pressure, calling on the department store chain to make changes to its board or face another proxy fight.

Macellum Advisors, which has a roughly 5% stake in Kohl's, is urging the company to replace three or more long-tenured directors, including its chair, after sale talks collapsed earlier this year and as the share price sags, people familiar with the matter said.