There is no 'Tyrant' trait in EAB other than vanilla's tyrant opinion modifier. Tyranny works on a by character basis, when a father dies all is forgiven for the new comer, just as it works in vanilla. The only change to tyranny I have made is the ability for a liege to exile an imprisoned kinslayer without incurring any penalty (save for a piety cost). I meant to add more stuff like that but work has gotten in the way.

Besides, I've never really liked the tyranny system in CK2+. It's just not for me.