Field level security settings are not possible: https://jira.atlassian.com/browse/JRA-1330
You could checkout the mentioned workarounds:
Higher in the thread Erik S makes a comment about a workaround that may be useful for some users:
it is documented further here:
Third party commercial plugin:
You can always use the Behaviours plugin: https://marketplace.atlassian.com/plugins/com.onresolve.jira.plugin.Behaviours
I'm using this to control who can insert information in specific fields either at issue creation or at issue edition.
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