Possible Clues:

• Can you think of a term for a flower that's also a family member from Down Under?
• 'Shhhh!'
• 'Keep it under your hat!'
• 'Don't tell a soul'
• Keep silent (colloq.)
• What's parent called? Keep it to yourself!
• ''Zip your lip!''
• "Hush!" to a florist?
• Complete silence is required
• Say nothing about who strummed