WASHINGTON—An Obama-era official at the Consumer Financial Protection Bureau sued the Trump administration on Sunday night to block budget director Mick Mulvaney from taking control of the agency.

Leandra English, a career staffer appointed Friday to lead the CFPB by former director Richard Cordray, filed the lawsuit in federal court the night before the bureau was set to reopen with dueling temporary leaders vying to take it over. In doing so, she touched off a legal fight that will trigger court interpretations on how different...