In the Automation section, you can select the "Add tag" action - and the selected tags will be assigned to the card when the event you defined occurs.
A new automatic action has come to replace the old default tags mechanism - you may have already seen our announcement. Your previous settings have been recreated as automations - you can edit, delete or expand them using other available actions.
You can set up automation so that the action is performed not only when the card is moved, but also when it is created - to do this, select the "Card moved or created in" event type. Please note that now you can specify the location of the card when defining an event more flexibly - select only a board, a specific column on it or a lane - and set up automatic actions at any level.
Now you do not need to specify a user when choosing this type of action - you can assign the author of the event as responsible or remove any responsible from the card.