How to let a client monitor progress of a specific Kanban card?

Unfortunately, you cannot share just 1 specific Kanban card or a few cards with an external user - a person that was not invited to join your Kanban Tool account.

The only solution is to add the client as a user of your account. You will be able to provide your client with a direct link to a specific Kanban card, but please note, they will also have a full view of the board the task is on. You can give this user a read only access privilege, preventing them from making changes to any of the cards.