Firstly you will need to ensure the new supplier exists in the Supplier Entry area. Next you should update the Candidate Entry record for this candidate to reflect which supplier they are currently working through - this will ensure that any new assignments are processed against the correct supplier.
On the existing assignment you should also update the 'Payment To' field to ensure the current supplier is attached:
The system will update any Open timesheets that have not yet had any activity on them with the new supplier. For any timesheets that have already started or are mid-process, you can update them at the point of validation - as long as the assignment the timesheets were generated from state the correct supplier at the point of validating those timesheets they will be re-attached to the correct supplier.
You can also do this post validation by selecting the candidate from the Timesheet Display area, selecting the timesheet(s) and clicking Update - this instructs the system to check again for any changes and should reattach the timesheet to the correct supplier.
If you have already paid timesheets to the old supplier you should credit or void these documents (this depends on what best suits your internal process) then raise correct timesheets for the correct supplier.