Apple Inc. is shaking up leadership and reordering priorities across its services, artificial intelligence, hardware and retail divisions as it works to reduce the company’s reliance on iPhone sales.

The changes, which can be traced back to last year, have included high-profile hires, noteworthy departures, meaningful promotions and consequential restructurings. They have rattled rank-and-file employees unaccustomed to frequent leadership changes and led Apple to put several projects on hold while new managers are given a...