How can we validate individual form field In Magento 2?

You can validate specific field using below code of line.

<script>
require([
  'jquery',
  'mage/mage',
], function($){
   $( "#new-button" ).click(function() {        
       $('input[name="field_mobile"]').validation();
       if(!$('input[name="field_mobile"]').validation('isValid')){
           return false;
       }
   });
});
</script>

NOTE: make sure you have added data-mage-init='{"validation":{}} in form tag.

I found this one to work:

$.validator.validateSingleElement('#input-id');

More about how it's implemented and used here: https://mage2.pro/t/topic/5504