Project Task Permissions
Even if the Advanced Project feature is enabled, users must have the Edit or Full permission for project tasks before they can create, update, or delete this record. For search, the user must have at least the View permission. NetSuite administrators can enable the Project Task permission for specific roles by going to Setup > Users/Roles > Manage Roles.
After you open a role for editing, note that the project task record is listed on the Lists subtab of the Permissions tab.