I let slip my teenager's secret to a relative, and now he doesn't trust me. What should I do?

Wounded trust can be rebuilt, but it demands time, honesty and patience from you. Start by admitting the mistake clearly without excuses, and apologise for the embarrassment he suffered. Promise to keep his secrets from now on, then keep that promise consistently, because words alone are not enough. Prove it with small actions: when he shares something, keep it to yourself and do not spread it to relatives or on social media. Give him time to heal and do not push for instant trust. Every time you keep a trust, one brick is laid back in the wall that once fell. Read educating the family.