Possible Clues:

• "I can't share that information"
• "Shh! Don't tell!" and hint to what can precede the starts of 18-, 23-, 37- and 52-Across
• 'Mum's the word!'
• "Don't tell anyone"
• 'Shhh!'
• 'Shhhh!' follower
• ''Mum's the word!''
• "No one can know"
• Quelling words
• What putting one's finger to one's lips may mean