There are a few ways to achieve this:
1. Reports > Jobs.
You can type in a client's name in the search field to bring up all the jobs done for them, and then Download CSV.
2. Jobs > Jobs List.
Enter the client's name into the search field, and then click Export.
3. CRM > All Contacts > Select edit arrow for specific client > Jobs tab.
You can simply select Export in the smart table.