Name the impact without exaggerating it
Describe who had to wait, worry, redo work, spend money, or make a choice with incomplete information. For a message about how to reconnect with a former client, use this factual base: remind the person where you worked together, when, and what current topic makes the contact relevant.
Make repair practical
Offer the repair you can actually complete, with ownership, timing, and any limit stated honestly. Make one modest request and give enough information for them to decline or redirect it. Make the immediate next step clear enough that the recipient can answer without reconstructing the entire history.
Let future behavior carry the proof
Do not imply endorsement, exploit a former hierarchy, or send confidential material from the old relationship. Use official business, privacy, conflict, and procurement rules when commercial or regulated information is involved. A promise inside a message is weaker than a visible change in what you do after it.