There was a system-level "Allow Assigned Tasks Only" option in the admin menu under "Timesheet Options" - don't think I've ever seen anything on a per-project level though?
Some discussions (that I don't really know the end-result of) around that here;
Allow assigned tasks only in Timesheet options : https://communities.ca.com/message/99672832#99672832
EDIT: actually that other thread says "Instead a new attribute named 'Prevent unassigned timesheet task' has been introduced for 'Project Object' which is false by default." so maybe thats just the answer, will depend of your Clarity version though.
EDIT AGAIN : and a much more detailed discussion can be found here ; CA Clarity Tuesday Tip - Prevent Users From Adding Unassigned Tasks