If no one is playing content from your Plex Media Server, there are a few common reasons for a "Plex New Transcoder" process to be running:
Video Preview Thumbnails Generation
The most common reason users will see this unexpected CPU usage is when they enable their Plex Media Server to generate video preview thumbnails.
If you have the Generate video preview thumbnails (advanced) setting enabled, then your Server will generate video preview thumbnails for new content.
Related Page: Plex Media Server > Video Preview Thumbnails
This process essentially requires a transcode of the media file in order to generate a series of screengrabs, which are then used to make the media index file. The process is CPU-intensive and can take anywhere from a few minutes to tens of minutes for a single item depending on both your processor power/speed as well as the duration and resolution of the media file.
If you enable that setting prior to adding a large amount of library content, you can expect the "Plex New Transcoder" process to be running and using a large amount of CPU for hours or even days.
Chapter Thumbnails Generation
When you add new content to a "Movie" library, one of the things Plex does is try to find chapter information to match that movie so that you can quickly jump to a desired chapter when watching it. If we find chapter information (either embedded in the file or from an online source), then we also grab some quick screenshots around the start of every chapter. Those screenshots can be used by apps when displaying chapter information to you.
In most cases, you'll hardly even notice this occurs. On most desktop computers, this would take just a few seconds, for instance. However, if you run your Plex Media Server on a low-powered computer such as a NAS device, then it's possible the process could take a fair bit longer and you might notice some high CPU usage while the chapter thumbnails are generated.
Preparing Sync Content
When you specify content to sync—either for Mobile Sync or Cloud Sync—then your Plex Media Server will first prepare that content to ensure it is in a compatible format. For the majority of content, this will involve transcoding the content.
Content transcoding is a very CPU-intensive process and can take tens of minutes for a single item in some cases. If you inadvertently select an entire library to Cloud Sync, for instance, then your Server is going to be trying to transcode the entire library to prepare it to sync.
You can check sync jobs that you've created in your Plex Web App.
Note: If you share libraries with friends and you've enabled Allow Sync for their share, they may have set content to sync, too.
If you have created any "optimization" jobs for content, then Media Optimizer might be using the transcoder to process and optimize content for you. If that is happening, then it will appear in the Conversion Queue.
Related Page: Plex Media Server > Media Optimizer