Possible Clues:

• Half speak unintelligibly, keeping this quiet
• She gets the chance to hold her tongue
• Closemouthed, about star's secret
• Not blabbing
• The word, as suggested by the saying formed by the ends of this puzzle's four longest answers
• Old woman's word for maintaining silence?
• Relatively tight-lipped?
• Keep her provided she's a chrysanthemum perhaps
• Lady sounding bubbly
• Tight-lipped old lady