If the bird of prey hovers in the sky it is likely to be a Kestrel since this is the Kestrel's main way of hunting the small rodents, reptiles and insects on which they prey.

 The male Kestrel above spreads its tail and flaps its wings rapidly while keeping body and head fairly motionless. Also note that, above and below, the eyes remain fixed on the target.

In addition to fanning its tail it uses its "thumbs" (halfway along leading edge of wing) as part of its aerial control system

Different Kestrel -- another male -- in UK