Presumably the client record has an email address field correct? You can use a lookup field to push that information from the client table to the form table. 

Hey ​@mmoon,

Fully agree with ​@DisraeliGears01. If your Clients table has an email field, you can look that up on the form submissions table. For further info on lookup fields you can check out this article.

Mike, Consultant @ Automatic Nation

In the table where form responses go, add a new field and set it as a lookup. Choose the linked client field and then select email as the value to show (assuming you have an email field in the clients table).

Now, whenever someone selects a client in the form, their email will automatically appear in that lookup field.

Taha, Airtable Advisor