No, .NET does not open up any new security risks for your computer. .NET is an application framework that Microsoft has developed for applications that for example, are created in Visual Studio using WinForms. To run those types of apps you would need to install .NET.
As far as I know, .NET itself won't cause any security issues, and it's mostly up to the developers to keep their apps safe and not have any weird code or poorly protected code. Something to keep in mind is that .NET applications are extremely easy to deobfuscate and view the source code using an application called dnSpy.