As people move around, or the point of interest in the picture changes, you normally need to reframe the shot to compensate. This might involve little more than a slight tilt to correct the headroom, or a simultaneous pan-tilt-zoom to tighten on a single person within a group shot.
The most successful camerawork always looks as if it has developed quite naturally from the action itself. If you alter the shot by reframing, tilting, panning, zooming or dollying on a motionless subject your audience will be aware of the change immediately. But make these adjustments while the subject itself is moving (even a head turn will do), and the camerawork will still be effective – but quite unobtrusive.