WASHINGTON—Pete Buttigieg’s presidential campaign is dealing with some departures in the closing days before the Iowa caucuses, as its head of talent and cybersecurity aides have left, and it still faces questions about staffer diversity, according to people familiar with the matter.

Nadia Singer, the talent director for the campaign responsible for identifying potential new hires, parted ways with the former South Bend, Ind., mayor’s team earlier this month, some of the people said. Ms. Singer, who previously worked at question-and-answer website Quora Inc. and Facebook Inc., was seen as part of a cadre of Silicon Valley hires by Mr. Buttigieg.

Her contract employment ended abruptly after she relocated to South Bend from San Francisco, those people said. Ms. Singer’s LinkedIn page shows she worked for Mr. Buttigieg between June 2019 and January 2020.

Two cybersecurity aides also left the campaign around the same time. The campaign described the staffers as midlevel.

A spokesman for the campaign said Ms. Singer’s contract ended because the campaign is fully staffed and not hiring during the primaries.