Jon Cave

If you don’t check your admin panel on your WordPress install very often (maybe because you prefer to use remote publishing) or you want to make sure 
that your clients’ WordPress installations are updated, then this is the plugin for you. You don’t have to login to your admin panel regularly, 
suscribe to an RSS feed, or do anything apart from installing this plugin to be notified when an update to WordPress is released.
All you have to do is install Update Notifier and forget it until you receive an email telling you to update.
To change Update Notifier’s options, go to Update Notifier under the main Settings menu. From there you can add a secondary email address 
which will also receive update notifications and you can activate update notifications for themes and plugins.

Update Notifier

Sends email notifications if a new version of WordPress available. Notifications about updates for plugins and themes can also be sent.

Scott Reilly

Tired of visiting your WordPress admin dashboard and having WordPress nag you about your web browser being out of date? Maybe you already know about it and want to hold off on an update and would rather not see the update nag so prominently on your dashboard. Or maybe you don’t want your site to bother your users about how up-to-date their browser may be. Activate this plugin and be bothered no more!
In most cases, your browser will already actively alert you to new releases if it doesn’t already update your browser for you in the background.
Benefits over simply clicking “dismiss” on the browser nag notice yourself when it appears:
<ul>
<li>This plugin prevents WordPress from making the network request to check if the browser is out of date. If you click “dismiss”, all you’re doing is hiding the nag; WordPress will still make the network request to check if the browser is out of date.</li>
<li>This plugin prevents the nag from appearing for all users to the admin area of the site. Clicking “dismiss” only removes the nag for the person dismissing it.</li>
<li>This plugin saves having to see the nag in the first place</li>
<li>This plugin saves having to click “Dismiss” to dismiss the nag</li>
</ul>
Of course I don’t condone using an out-of-date browser. Such a browser puts your computer and data at potential risk. You are often better served with the latest version of your browser: improved security, improved performance, improved stability, and additional features. However, there are situations where you cannot upgrade in a timely fashion, or you are intentionally holding off on upgrading (e.g. as you wait for a bugfix release, or for browser plugins to update their compatibility).
Links: <a href="https://coffee2code.com/wp-plugins/no-browser-nag" rel="nofollow ugc">Plugin Homepage</a> | <a href="https://wordpress.org/plugins/no-browser-nag/" rel="ugc">Plugin Directory Page</a> | <a href="https://github.com/coffee2code/no-browser-nag/" rel="nofollow ugc">GitHub</a> | <a href="https://coffee2code.com" rel="nofollow ugc">Author Homepage</a>

No Browser Nag

Removes the browser nag that appears in the admin dashboard when using a less-than-current web browser.

Update Notifier vs No Browser Nag