Possible Clues:

• Called round at one time, full of self-importance
• Vain
• 'Con thought so much of himself that he didn't get to his feet, by the sound of it (9)'
• Narcissistic
• Excessively vain
• Called without once becoming stuck-up
• Vain, having swelled head
• Study 29's broadcast in vain
• Anything but modest once called outside
• In vain mentioned hiding in the past