Since this game is similar to football manager maybe the attribute is similar too, in football manager:
Aggression
How likely a player is to choose to get involved in a physical situation and how much he exerts physical force in such situations. Physical situations include attempting to tackle an opposition player, marking and competing with an opposition player to get to the ball.

so I think aggression is good to have for defender, my best defender have high aggression (165%) and never get a card (not even 1 yellow!). I also have defender that have 196% aggression that never get a card and other defender with 119% aggression with more card than the other 2 (3 yellow this season) so its unrelated to defender dirtiness imo.