In order to hide the Create Issue option in the drop-down menu of the JIRA application top bar, as shown in the following screenshot:

You can perform the following steps:

1. Login as an Administrator to your JIRA application instance
2. Navigate to System > User Interface > Announcement Banner (Alternatively, you can click on g+g keyboard shortcut and type Announcement Banner)
3. Add the following JavaScript to your banner, and click on Set Banner

<script>
jQuery(document).ajaxComplete(function(event, xhr, options) {
    if(options.url.indexOf('find_link') > -1) {
        jQuery('#issues_new_issue_link').hide();
    }
 
 });
</script>

After doing that, now the option should be removed from the drop-down menu, as the following screen-shot:

Note: Credit to  Akin Gumusel who shared this resolution with us.