The Harris Hawk, owned by Jim Gordon and Alex Bolton, escaped from their house in the town on Saturday (May 13).
The five-year-old male – called Tuck after the Second World War pilot Robert Stanford Tuck – has been spotted on Neatherd Moor and in other various locations since his escape.
Mr Gordon said: “We’re really hoping that he’s going to get hungry enough to come back and get some food.
“Although we know that it will probably eat whatever it can get – and will definitely hunt as many rats as it can.”
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The hawk can be distinguished by a disfigured talon on its right foot after a hunting injury.
Harris Hawks breed in the southwestern United States and South America.
Their carnivorous diet consists of small creatures including birds, lizards, mammals, and large insects.