Have a look at the Data Source pane. You'll notice your Access db has two sets of fields: "q" and "d". That's Query and Data. You want to pull the Query Client ID into the form, then query off that. The data will then pop in.
I'll tell you how I like to do it. I like to make the query field a drop-down so the user can choose from a pre-determined list. In the Access mdb I create a query that returns just (as you said) Client ID. Then, I make that a secondary data connection in the InfoPath form.
I would drag over the Client ID query field, and change it from a text box to a drop-down list, then assign that dropdown list to have the secondary data connection as the data source.
Next, drag over the "Data" detail records into a table or section. Finally, set it so that when the data changes in the dropdown control, the db is queried. Do that with a rule. Alternatively, you could make a "Go" button whose rule is to query the db.
Now, the user opens the drop-down, finds the proper Client ID, that control changes, and the db is queried.
If you have a lot of Client IDs, then a dropdown would not be appropriate. In that case, the user would just type it in, but you still have the principle that if that control (a text box) changes, then the db is queried.