Database design - do I need another table?
Another option is to just add StartDate and EndDate fields to your "Employment" table.
Then when a client comes in with a change in Employer you update the EndDate for his previous Employer and add a new record for the new Employer with no EndDate. You can always look up his current employment by checking which record for that ClientID has no EndDate. If you don't need start dates or end dates you could just add a field that's basically a flag to indicate whether this is present or past employment.