Let's say on a board we have two lists. List
B. Whenever a item get's dragged from any list to list
B, I'd like it to be assigned a specific label (and removed others if they are set).
Is there any way to do this?
You can use the third-party automation tool Butler for Trello to do the job for you.
Use the Triggers and Actions panel to enter your command
when a card is added to list "B", remove all the labels from the card, and add the "Specific" label to the card
Test to make sure it works, and you're off to the races
Here's how it looks in action