The Trending content widget uses the widget_trending_content template to render each item. By default, it displays the thread's creation date ($thread.post_date). To show the most recent post date instead, you need a template modification.
Go to Admin Panel > Appearance > Template modifications and create a new one:
Template:widget_trending_content
Search type: Regular expression
Find:
\$thread\.post_date
Replace:
$thread.last_post_date
The last_post_date field is already available on the thread entity — it stores the timestamp of the most recent reply. So the replacement should work without any additional data fetching.
If the template uses <xf:date> or {{ date() }} to format the date, just swap the variable inside the function call while keeping the formatting the same.
One thing to note — if you're using the default XenForo 2.3 trending widget, first inspect the actual template name by hovering over the widget with debug mode on (add ?_debug=1 to the URL). The template name may differ slightly depending on your version.