Kinda, it doesn't prevent the move but it undoes it if the wrong member does it..
Say you only want member called "@member1" to be able to move cards into "List A"
You can do an automation:
when a card is moved into "List A" by anyone other than "@member1", move the card to list {triggercardpreviouslistname}
I often add to the end of that automation:
and post comment, "Whoops @username, you didn't have permission to move that."
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