Sadie, thought you might like that!
You could have a sit-down with him/her and ask a few key questions. How do they think things are going, do they have any complaints, and hear them out.
That might help you to understand if they are a run of the mill manipulator, or have something else going on.
You don't have to DO anything, or promise anything, but simply listen to assess where their head is at.
Then act accordingly, right?
Entitlement--treat them no differently than all the rest, and make it known to them that they have no special privileges.
Negativity--if unwarranted, you can put the heat on them with another sit-down that they need to change their attitude, that it is not good for the company, and that it is unwarranted.
I'd just rule out legitimate complaints first.
Then they'll know you're onto them and their game isn't going to work anymore.