In order to transfer ownership to a team, the user has to be part of that team already. If the user is not part of that team, a team owner can invite them to join their team. They can invite users in two ways: by email or by Salesforce username.

In Gearset, navigate to the My account page, and make sure Team management is selected on the left.

To invite a new team member, either enter their email address, or (if applicable) the Salesforce username they use to log into Gearset.
Click the Invite via email button to send the invite. The user will receive an email inviting them to join your team. If they don't already have a Gearset account, they can create one. Once finished, the user will be added to the team.
Any outstanding invites will be shown on the My account Team management page. Invites that have not been accepted will expire in five days.
You can also copy the direct invite link from here if there are any issues with the email invite.
Once the user accepts the invite, they will be added to the team and listed in the team table.
Note: Gearset users can only be a member of one team at a time. If you belong to a team and accept an invitation to join a new team, you will leave the original team. Any deployment history you have will remain accessible from the old team only - it will not be transferred to your new team.

Changing a user's role and assigning license.

A team owner can manage the roles of the remaining team members (including the other team owners) in their team.

To change a team member's role, select Change role... from the My account Team management page.

In the dialogue box that appears, select Owner or Member as required, and click Save.

That user's role will then be updated in the app and will be displayed in the team details table.
If you have available licenses, assign them a license by changing the license type from None to Starter, Teams, or Enterprise, as shown in the picture above.
Make them a team owner. (You can have multiple team owners per team.)