使用传递给#T1更改处理程序的date对象(time)；在该时间基础上添加2小时（以毫秒为单位，因此2*60*60*1000)，并创建一个新的date()对象。在此基础上设置#t2。

$('#t1')
  .timepicker('option', 'change', function(time) {
    var later = new Date(time.getTime() + (2 * 60 * 60 * 1000));

    $('#t2').timepicker('option', 'minTime', time);
    $('#t2').timepicker('setTime', later);
  });

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$('#t1').timepicker({
  timeFormat: 'hh:mm a',
  interval: 30,
  minTime: '8',
  maxTime: '11:00 PM',
  startTime: '08:00 AM',
  dynamic: false,
  dropdown: true,
  scrollbar: true
});

$('#t1')
  .timepicker('option', 'change', function(time) {
    var later = new Date(time.getTime() + (2 * 60 * 60 * 1000));
    $('#t2').timepicker('option', 'minTime', time);
    $('#t2').timepicker('setTime', later);
  });

$('#t2').timepicker({
  timeFormat: 'hh:mm a',
  interval: 30,
  maxTime: '11:00 PM',
  startTime: '08:00 AM',
  dynamic: false,
  dropdown: true,
  scrollbar: true
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/timepicker/1.3.5/jquery.timepicker.min.js"></script>

<link href="https://cdnjs.cloudflare.com/ajax/libs/timepicker/1.3.5/jquery.timepicker.min.css" rel="stylesheet" />

<input type="text" id="t1" />
<input type="text" id="t2" />