I am assuming the client names are unique.
If not you would want to do ensure this happens.
Airtable provides you with a Autonumber field which would be helpful in creating the unique client names
After that I would suggest that you break down your table containing the client name and contract date into 2 different tables.
1.Client Table
2.Contract Table
Use the linked record feature of Airtable to create a relation between the Client and Contract table.
Now add in another table called Invoices.
Associate the Invoices table with the Contract table now.
After that you can use a lookup field to show the correct contract on the Invoices or Client Table.