To achieve the desired result, you could extract the default control template of the RadTabControl element, and add a new button inside the ScrollViewer control, with x:Name="ScrollViewerElement". After that, create a new Style with TargetType="RadTabControl" and set the modified template to its Template property.
Please note that if the Xaml version of the assemblies is used, each StaticResource present inside the default control template would need to be extracted as well. Otherwise, an exception will occur for the missing resources.
Regarding the functionality of the included button, you could bind it to a command inside your view model. Through this command, modify the collection bound to the ItemsSource property of the RadTabControl element.
Alternatively, if the abovementioned approach is undesired, you could take a look at this article from our documentation, which shows an example of how to include such a button inside each RadTabItem element. Furthermore, the Closable Tabs SDK Example provides a runnable example of the approach from the provided article. The example could be found in our SDK Samples Browser, or in our GitHub repository.
With that said, I have attached a sample project, that contains an implementation of the first suggestion, so, could you give it a try?
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