Hi Alexander,
As far as I know, there is no out-of-the-box method to stop the rendering thread from ticking. This is because we need to do some bookkeeping while the process is suspended; otherwise, the engine will run into stability issues. However, there is the GameViewportClient::bDisableWorldRenderingflag, which, if set, allows you to save a lot of system resources while you have the application in the background. Toggling this flag could be a good alternative solution for you. Please let me know your thoughts on this.
Cheers,
Tim