Labor Secretary Alexander Acosta will soon lose another valued member of his inner circle when Chief of Staff Molly Conway leaves the department in the coming weeks, according to sources familiar with her plans.

A Labor Department spokesman confirmed Conway’s impending departure.

Conway has been telling people she’s headed for the exit this summer, even though she was just promoted from deputy chief of staff at the start of June. She’s also been serving in a dual role as acting head of the Labor Department’s Employment and Training Administration.

The move means Acosta will lose one of his longest tenured...