If the Worksite has been submitted or accepted, you will have to create a revision, before following the instructions below.

If the Worksite is a draft or an not yet submitted revision, you can click on the 'Switch project' button in the Worksites Details panel to go back to the Worksite Ownership page, where you can update the Worksite's Client and Project. Please note that Projects are linked to Clients, so if the Client has changed, you're likely to have to create a new Project under this new Client.