As the title suggests, instances may exist when you want to use Googles services even though you operate a handset which has Google PlayServices removed.
I recommend one of two approaches for this; both of which provide effective solutions without the hindrance of Googles far-reaching data grabbing techniques.
Option 1: GApps Browser
This is an excellent, lightweight app you can download directly from F-Droid. This app is a privacy-focused sandbox which opens up Googles web services, such as email & calendar, in a security-hardened web browser.
GApps Browser runs in it's own sandbox, with 3rd party requests (images, scripts, iframes, etc.) blocked, and all external links opening in an external default web browser (which should have cookies, plugins, flash, etc. disabled).
I especially like this solution. Besides offering a service which was off limits previously, it does so in a way which runs very smoothly even on older technology & has zero special permissions to provide so it really is secure.
Option 2: K9 Email Client
Some users prefer to access their emails via an email client such as the Gmail App or Outlook. Since the Gmail app is off limits I recommend the highly regarded K9 Email client. New Omerta handsets will include this email client but older devices can access the app from this link: https://f-droid.org/en/packages/com.fsck.k9/
The K9 email client can connect to your Gmail account using IMAP or POP protocols & full instructions for configuring K9 to Gmail is found here: https://k9mail.app/documentation/accounts/providerSettings.html