Possible Clues:

• 'You've divined that one's staying, by the sound of it (7)'
• Visitor, on being announced, perhaps got in one
• On the radio, visitor conjectured
• Through the ear, visitor took a shot
• Fancied hotel client in audition
• Assumed visitor is to be announced
• Acted desperately on "Jeopardy!," perhaps
• Acted desperately on 'Jeopardy!,' perhaps
• Estimated correctly
• Outspoken visitor, it's supposed