To render multiselect fields with fancy component like rendered in jira, add following js to description field. Replace <id> with custom field ID

gistfile1.js

<script type="text/javascript">
(function($) {
    AJS.$("#customfield_<id> option[value='-1']").remove(); //Removes the default value "None"
    function convertMulti(id){
        if (AJS.$('#'+id+"-textarea").length == 0){
            new AJS.MultiSelect({
                element: $("#"+id),
                itemAttrDisplayed: "label",
                errorMessage: AJS.params.multiselectComponentsError
            });
        }
    }
   
    AJS.toInit(function(){  
        convertMulti("customfield_<id>");
    })
   
    JIRA.bind(JIRA.Events.NEW_CONTENT_ADDED, function (e, context) {
        AJS.$("#customfield_<id> option[value='-1']").remove();
        convertMulti("customfield_<id>");
    });
})(AJS.$);
</script>