If the Client Hours field appears read-only on a time entry, your Security Profile does not have the Allow edit client hours permission enabled. This permission controls whether a user can directly edit Client Hours independently of Actual Hours.
To check or update this permission, a Full Access user can go to Settings > Access & Permissions > Security Profiles, open the relevant profile, and look for Allow edit client hours under the Time & Expense - Time Entry section.
Note: Even without this permission, Client Hours still auto-syncs to match Actual Hours when you update Actual Hours unless Client Hours has already been set to a value different from Actual Hours. In that case, the existing Client Hours value is preserved, and the divergence indicator on the Client Hours field shows the difference between the two values.
For more information on the difference between Actual Hours and Client Hours. Check CORE Help Center for details.