Possible Clues:

• There's an excessive turn in her, by the sound of it
• In a car one needs the press for the sound of it
• Uphill stone pusher (Gk. myth)
• Owl beak
• A horned owl?
• Unhappy audience member, maybe
• The owl starts to be in the beginning of 32 across
• Warning sound of an owl?
• Look to 20 down for this sort of an owl, perhaps
• The owl in the car?