Possible Clues:

• Precipitate way the staff leave school assembly?
• Impetuously
• Precipitately
• *One way to dive in, or a theme hint
• Primary principal previously precipitate
• I fret and dash off without thinking enough
• A couple of chiefs combined recklessly
• If trashed, dive as divers usually do
• Principal leading impulsively
• Newspaper tycoon's written about daughter, though on reflection, recklessly