Gearset has full support for spinning up and deploying to/from scratch orgs - you can read more about that process in the scratch orgs configuration walkthrough.
Adding scratch orgs created outside of Gearset
You can use a scratch org created outside of Gearset, but it is less straightforward, due to Salesforce API limitations.
You would need to create the scratch org and then reset the password. To find out how to do that, click here.
Once this is done, you should add it in Gearset as a sandbox org in the Connections page, using custom domain.
It won't be automatically deleted when it expires, so this is something that has to be done manually.
Accessing scratch orgs created in Gearset, via the CLI
If you've created a scratch org in Gearset and now need to access that in another tool, such as the Salesforce CLI or Visual Studio Code, then you can do that by resetting the password for the scratch org. For more information, click here.