There are two options to update Google Play Services: you can enter the Play Store or access our website.
Update Google Play Services from Google Play
To update the app from the operating system, first, access the Android settings and go to the Apps & notifications menu.

Click App info.

Find the Google Play Services list and click on it.

Scroll to the bottom of the screen and click App details.

You will be redirected to a Google Play Store window. If a green Update button appears, it means your version is outdated, click it to install the latest available version as you would any other app. If any button other than that appears, it means you have the newest version and do not need to do anything.
Problem-solving
If, for any reason, you do not see the Update button, but you are sure that there is a new version, try to clear the Google Play Services cache and data. Go to settings like before, find the list of apps, and click on Google Play Services. Then click on the Storage option.

Then click Clear Cache.

Now tap on Manage Storage.

Clear all data.

Finally, go back to the Google Play Store, wait 5 minutes, and try to download the update from Google Play Services again. To do this, repeat the steps above, but on the Google Play Store app that you have installed
Update Google Play Services from Malavida
Another option to update this app is using our website. On your smartphone, access settings. Enter Apps & notifications, find Google Play Services, and sign in. Scroll all the way down to see the number of the version you have installed.
Then, visit our Google Play Services dedicated website and check the number of the version we offer against yours. Is it the same? That means you are up to date, so you can stop reading here. Conversely, if the number on your phone is lower than the one on our website, you need to update it. Click on the green Download button that we offer on our website or at the end of this guide (if this is the first time you do that, Android will first ask you to give installation and apps permissions to the browser).

When the APK is completely downloaded, click the on-screen notification or visit your download folder to start the installation of the updated version by clicking on the file (if this is the first time you install an APK from the notification of your browser, the system will request permissions for that browser to install applications.

The fact is that you will rarely need to update Google Play Services manually on your phone. It is a basic system app that acts as a bridge between Google's apps and services, so the very operating system is constantly checking that you have the latest version. It is the only way to guarantee the best possible performance of your phone.