Background

Currently there is a feature request for this:  GHS-9695 - Getting issue details... STATUS  

However, administrators who want a workaround until the feature is implemented can follow this article. 

Resolution

• We can use CSS to forcefully hide the priority icons.
  This is considered a customization to JIRA, hence Atlassian will not be able to provide technical assistance if the code causes incompatibility issues.

• Open the JIRA Announcement Banner via Administration >> System >> User Interface >> Announcement Banner

• Add the following code to the announcement banner:

  <style type="text/css">
  .ghx-priority { display: none; }
  </style>

  Save the changes.

• Refresh your Agile board, and you should be able to see the priority icons being hidden:
  Plan Mode:
  
• Work mode: