[Django]-X-editable – run code after successful POST?

Use the success param of X-Editable

$('#issueResponse').editable({
    success: function(response, newValue) {
        $( "#Response" ).load( "../ajax/get/{{issue_obj.id}}/response/" );
    }
});

Or you can add an event trigger

$('#issueResponse').on('save', function(e, params) {
    alert('Saved value: ' + params.newValue);
    $( "#Response" ).load( "../ajax/get/{{issue_obj.id}}/response/" );
});