Depends upon species and exactly what a "bird of prey" is.
The term "bird of prey" ought to mean any predatory bird catching animals big enough to be called "prey" rather than just "wriggly food". However, the term is usually restricted to birds in the hawk, eagle and vulture group, the Falconiformes. Some of these actually eat snails, insects, worms, carrion or even fruit, but most do eat larger prey.
These birds usually hunt any time during the daylight.
Owls are also predatory, but are a different family. Most of course hunt at night or at dusk, but a few are day-fliers (some or all the time).
Then there are lots of other predatory birds (some quite hawk-like) such as shrikes, crows, kingfishers, gulls, skuas, storks etc etc.