1. Head to the Project Setup page
2. In the Clients section, if there is more than one client on the project, there will be a "Make Primary" link next to any clients who cannot clear updates. Click that link to make that individual the one person on the client side who can clear updates on that project.
3. CoConstruct will not send a notice to that person, so you may want to post a message to let that client know that he or she can now clear updates.