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There is a leadership style called "coaching" I feel would be very appropriate for this situation. In this case, you have people with good knowledge of their jobs but not motivated. One of the things I do is have them see the big picture, on why it is necessary for this job tasking to get done. Also, if needed, I would add value to their work; in other words, show them their work is an absolute must for mission accomplishment which can help motivate them as well.
