This usage implies exploiting or using someone for personal benefit, often seen negatively. Don't just trade on your friend's connections without giving back.
Pro Tip 2/3
Reputation Leverage
People or companies often 'trade on' their good name to attract opportunities, based on past achievements. The restaurant traded on its Michelin star to draw in crowds.
Pro Tip 3/3
Subtle Manipulation
'Trade on' can suggest subtly using a trait or feature to maneuver situations in one's favor. She traded on her charm to win the negotiation.