New boss from outside – overseeing staff who wanted the job

Scenario: A new IT boss is hired from outside of the company. Some of the current staff, who’ll be direct reports of the new boss, had applied for the job, but they were turned down because the external candidate had stronger qualifications. Current staff who wanted the company to promote from within could experience resentment and reduced morale.

What’s your advice for the new boss for handling the situation?