Even if you can't offer promotions, there are always some activities that can offer overqualified employees the opportunity for development. Find them some administrative or organizational tasks or even individual projects which will enable them to acquire new knowledge and skills.
First of all, find out whether your overqualified employees are happy that they can perform a less demanding job, or whether they want more challenges. If they want a challenge, give it to them. The best projects for overqualified employees include stretch projects or any activities that forces them to step out of their comfort zones and show they can do more. Then give them more freedom to do their work. They will not need close supervision in most cases.
Overqualified employees may come up with many ideas to make things better. If you do not listen, they will soon become frustrated. That is why you should allow them to come up with possible improvements and also to implement these ideas in practice. Turn frustration into innovation.
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Article source Recruiter.com - a U.S. career and employment website