SQL Server 2016 - unexpected privileged time bursts
From an article on the internet:

(emphasis mine)  


  The Processor(_total)\ % Privileged Time counter shows the percent of time that the processor is spent executing in Kernel (or Privileged) mode. Privileged mode includes services interrupts inside Interrupt Service Routines (ISRs), executing Deferred Procedure Calls (DPCs), Device Driver calls and other kernel-mode functions of the Windows® Operating System.
  
  Most of the time a processor should be executing User mode operations, a high % privileged time might indicate a poorly written device driver or a faulty piece of hardware.


Reference: Windows Performance Counters Explained (AppAdminTools)

You might want to have a look at the DLL executing in the context of the CLR. It may not be releasing all its resources.

Equally interesting the information from Microsoft | SQL Docs:

(emphasis mine)


  Processor: % Privileged Time
  
  Corresponds to the percentage of time the processor spends on execution of Microsoft Windows kernel commands, such as processing of SQL Server I//O requests. If this counter is consistently high when the Physical Disk counters are high, consider installing a faster or more efficient disk subsystem.
  
  
    Note
    
    Different disk controllers and drivers use different amounts of kernel processing time. Efficient controllers and drivers use less privileged time, leaving more processing time available for user applications, increasing overall throughput.
  


Reference: [Monitor CPU Usage][] (Microsoft | SQL Docs)


Ensure your disk drivers are up to date
Ensure your disk I/O is ok
Remove any other services/applications from the SQL Server (instances)