Possible Clues:

• The cat doctor predates over 16 down
• Feline employer of the medical officer, perhaps (6)
• Cat that's good at catching small rodents
• Cat right to follow timid person
• Tom's second employer
• One employing doctor as pest controller
• Cat -- one in deep thought about nothing?
• One getting rid of vermin has way of working with consumer
• Cat helping with extermination
• Hunting beast exposed gruesome wound