The person who introduced you may be wondering whether the connection worked. They do not need the full story of a private conversation. They need to know you took care of the introduction.
A useful update can be one sentence: we connected and have a next step. If the work did not fit, say so. If you have not reached the person, explain the next attempt you plan to make without turning persistence into pressure.
Keep the client’s circumstances, terms, and personal information out of a casual update. The goal is to close the communication loop. Share only what is appropriate and agreed.
Thank the person for the judgment they put behind your name. Make the thanks specific. ‘The context you gave me helped us start with the right question’ is more useful than a generic acknowledgment.
Before the next meeting, review one introduction you gave and one you received. Find the missing next action. Complete it or explain clearly why it will not happen. Trust has a better chance to grow when people know where things stand.