Possible Clues:

• It is he that is praying and preying
• Green insect-eater
• It's himself that's not praying but preying
• Roach's cousin
• This insect makes a chap sit up
• Frenchman upset saint, one appearing to be praying
• Insect that's 'praying'
• Insect with a name from the Greek word for 'prophet'
• Termite cousin
• Cousin of a cockroach