it doesn't work because the js that attaches the timepicker to the html runs at document.ready, but the content loaded via ajax is loaded after document.ready
so you need to call the method that attaches the timepicker again after the ajax request has completed
you can try this:
$(document).ajaxComplete(function(event, xhr, settings) {
alert('an ajax request completed');
$('.time-picker').timepicker();
});