You'll need a more sophisticated table structure than "one record per client". How much more sophisticated depends on your needs. You'll need at least these tables and relationships:
Client---<Invoices----<TimeRecords ( ---< means "one to many")
Client::ClientID = Invoice::ClientID
Invoices::InvoiceID = TimeRecords::InvoiceID
Client::ClientID and Invoices::InvoiceID would be defined as auto-entered serial numbers.
You'd use a portal to Time Records on your invoices layout to log each time entry and a field in the layout would be configured as a drop down or pop up for selecting the client to be billed for that invoice. A typical time record would log the start and stop timestamps (This logs date and time in one field) with the elapsed time computed and then multiplied by your billing rate to compute a total for that time record. Either a calculation field in Invoices or a summary field in TimeRecords can be used to compute the total charge for each invoice.
This allows you to make multiple time records for a single invoice and multiple invoice records for a given client. You may also need a "job" or "project" table if you perform multiple jobs for the same client.