To add a new members to a Teams chat can be don the the Team itself.
When viewing the group you want to add someone to go the left pain of the window and hover the group name.
From here go over to the three dots and click on them and go down to add members.
From here all you will need to do is fill in the member you will want to add by entering their Email address. They will then get an Email to say that they have been added to the group.