Remind them of the shared chapter
Name the team, project, and period you worked together, then share a brief update. A specific memory is warmer and more credible than a generic networking message.
Separate reconnection from the request
If you need advice, a reference, or an introduction, state it plainly. Include the deadline and enough context to decide, and make no response or a no genuinely acceptable.
Keep the connection reciprocal
Ask what they are working on and follow through when you can help. Professional relationships last when contact is not limited to moments when one person needs something.