You would normally expect a user with Contribute access to be able to add web parts to pages and the likes in SharePoint but this isn’t always the case depending on your current security settings in the SharePoint Central Admin.
This is a problem I came across recently and here’s how I fixed it.
- Contribute level users do not have permission to add Scripting Web Parts to SharePoint pages.
- Access the SharePoint Central Administration website.
- Navigate to the Application Management section then click Manage web applications.
- Click on the relevant Web Application (this will likely be the one showing the URL you use to access SharePoint)
- In the Security section of the ribbon click ‘Web Part Security’
- In the popup window in the ‘Scriptable Web parts’ section check the “Allows contributors to add or edit scriptable Web Parts.” checkbox.
- Click OK to apply the change.
Warning: This will somewhat open up the security of your SharePoint deployment as contributors will be allowed to modify Scriptable Web Parts
Further information on this can be found on the Microsoft page. – https://technet.microsoft.com/en-us/library/hh272821(v=office.14).aspx