Do I need to have separate web hosting in order to use Google G Suite for my email?

You can run G suite without any hosting.

You’ll need to set up a few things with your registrar (the company you registered your domain with). The biggest one is MX records, which just tell your email where to go.

Here’s a quick article from Google
Set up MX Records for G Suite and Gmail

On the right, they have a few other linked articles as well, including some steps specific to popular registrars. There may be a few other things to set up, like if you want to use https://mail.yourdomain.com as your starting point for email that will need to be set up, but the basics are the same, you set up another DNS record with the registrar.

So you can cancel the hosting, just make sure you keep your domain registration and have access to those DNS records.

This is some of the more confusing stuff about the web. Feel free to post here if questions come up.

The term host is confusing above.

You DO need to pay someone to host the domain (the registrar as funkdaddy writes above).

That can be Google Domains or your current host or any of the countless others.

Then, as funkdaddy describes, you then point that domain at Google’s email servers.

You DO NOT need web hosting, meaning space on a server to keep a web site.