Use when discretion is important; revealing actions or plans could be harmful or spoil a surprise. They recruited new team members on the quiet to avoid alerting their competition.
Pro Tip 2/3
Not Underground
Does not imply illegal activity, just actions done without public knowledge. They donated a lot of money to the school on the quiet.
Pro Tip 3/3
Subtle Distinction
More secretive than simply 'quietly'; it suggests almost no one knows, not just being low-key. He's been writing a novel on the quiet, almost nobody knows.