Possible Clues:

• She had one hyacinth and the Greeks called her a muse
• Annual award named for a Muse
• Ad's award
• 51 in company of Muse
• Muse of history (from Renault?)
• Muse on carbon, fossil fuel being rejected
• Mother of Hyacinth, in myth
• Muse about regal animal losing tail
• Jingle award
• Award with a 'Billboard' category