Add class to {{ link }} twig attribute
I think your easiest approach would be to modify the field template and add a wrapping span with classes you need.

field--field-name.html.twig:

{% for item in items %}
  &lt;span{{ item.attributes.addClass('my-class') }}&gt;{{ item.content }}&lt;/span&gt;
{% endfor %}


or replace span and content with to add class directly to &lt;a&gt; tag:

&lt;a href="{{ item.content['#url']}}" class="my-class"&gt;{{ item.content['#title'] }}&lt;/a&gt;