Google on multiple selection listbox. Here's an example of what you'll find:
KB827423 How to retrieve the selected items in a multiple selection List
Box as a comma-delimited string in Microsoft Access
http://support.microsoft.com/kb/827423
Edit - You could then construct the appropriate SQL update or insert statement ... Where [client] IN that comma-delimited string.
Edit2 - check that last advice. The IN clause requires a list of comma delimited values, not a single string containing commas. Instead of constructing the string, may need to run the SQL action statement each time through the loop.