Note: Additional details provided here by poster have been moved to the question
You should look into CROSSTAB (Pivot) queries in MS Access for this. Once you understand the concept behind the CROSSTAB, MS Access has a query wizard that can build the query for you.
I'd suggest you put all the employees in one table:
| employee_id | employee_name | employee_other_fields |
+--------------+----------------+------------------------+
| 001 | employee_one | whatever else you need |
Clients in one table:
| client_id | client_name | client_other_fields |
+--------------+----------------+------------------------+
| 001 | client_one | whatever else you need |
And possibly a lookup-table to link the clients to employees, though you might consider just using a foreign key in the clients table, if you're sure there will never be, or could never be, a many-to-many relationship between clients and employees.
I imagine that the huge number of queries is a result of the table-per-employee design, whereas the three-table scheme should allow for simple -small and fast- queries (certainly relative to the existing structure). Obviously this might not work for your use, especially if it requires a lot of conversion and re-entry of data, so I'd suggest converting a sample quantity to the three-table format -or any other scheme suggested in the answers- and test whether or not the cost in time of changing the system is recouped by the efficiency/improvements of any change.