Bottomline, the head of state police is an appointment, serves the governor as long as the governor retains trust & faith in his judgement. Any governor can hire & fire their own staff/head of departments at their own descretion; end of story.
I'll repeat what I've written on other threads:
Palin offered Monegan (the former DPS commissioner) another job, at the same pay. He turned it down, then started making these accusations. Palin remained silent about her rationale for doing removing Monegan from the DPS position.
She has since explained why: Among other things, Monegan was going behind her back and lobbying for more funding from the legislature, at the same time she was trying to control costs. Monegan hadn't even filled all the state trooper positions he already had finding for, and he was still pushing for more -- undermining her authority.