You can allow specific Jira users or groups to edit the custom fields of the users. For instance, a manager or your HR department. Follow these steps to grant edit permissions to a user or group:
Log on as a Jira admin
Navigate to Jira Settings > Apps > PROJECT TEAM > Permissions page
Add the group or user to the list
Click Save
Regardless of these settings, Jira users are allowed to edit the custom fields of their own Advanced Profile page. Also, Jira administrators can edit the custom fields of any Jira user.