MacSteini

Many users still browse with outdated browsers, often unaware of the risks. Upgrading ensures better security and reliability. This plugin displays a subtle notification prompting visitors to update their browser. Activate the plugin, and it works seamlessly.
Visit <a href="https://browserupdate.org/" rel="nofollow ugc">browserupdate.org</a> for more details.
Want to help translate this plugin? Visit the <a href="https://translate.wordpress.org/projects/wp-plugins/wp-browser-update" rel="nofollow ugc">WordPress Translation Project</a>.
<h3>Important Notice</h3>
Breaking Changes in Version 5.0 
– Requires PHP 7.4 or newer. 
– Ensure your hosting is updated to PHP 7.4 before upgrading to version 5.0 or newer. 
– Servers running older PHP versions are no longer supported. 
 – If your server is running an earlier PHP version, please download <a href="https://downloads.wordpress.org/plugin/wp-browser-update.4.8.1.zip" title="Download WP BrowserUpdate from WordPress.org" rel="nofollow ugc">version 4.8.1</a>.

WP BrowserUpdate

Used for a client who had this exact request. Worked well.

Works as expected

This plugin notifies website visitors to update their outdated browser in a non-intrusive way.

Geoffrey

This plugin adds a message before or after (or both) your post content when this post is outdated. 
You visitor knows when a post is a little bit outdated and reads the content keeping its age in mind.
Features
<ul>
<li>Choose the place where the message is displayed (before or after the content, or both)</li>
<li>Choose which type of posts that are concerned</li>
<li>Custom delay for each post</li>
<li>Hide the message for a specific post (directly from the edition page)</li>
<li>Shortcode and template function</li>
<li>Lots of hooks (for developers)</li>
</ul>
A full documentation is coming.
If you find a bug, please, <a href="https://wordpress.org/support/plugin/juiz-outdated-post-message" rel="ugc">tell me</a>!
You want to translate this plugin and have your name in this page? Find translation files <a href="https://plugins.svn.wordpress.org/juiz-outdated-post-message/trunk/languages/" rel="nofollow ugc">here</a>.

Juiz Outdated Post Message

Simple to integrate, best practice for bloggers ! This plugin is on my toplist ! :)



Nice feature and easy to use

I've already said that to a lot of people, this one is a MUST HAVE.



great idea, UX topissimo

Works like a charm! 

If you want to use the shortcode in your template, do it like this : 
<?php echo do_shortcode('[outdated]'); ?>

Works with WP 4.7.x

This plugin adds a message before or after your post content when this post is outdated

WP BrowserUpdate vs Juiz Outdated Post Message