I am not talking about justice being served in a trial.
I read a bit about the Brehon laws, that capital punishment was extremely rare, and I am curious what happened if a person of higher standing (a king, for example) killed someone (a commoner) impulsively, let's say for revenge. What would his punishment be in this case? Would he be punished at all?
And what if the victim was his kin, a brother or a nephew, so someone (fairly) important?
I hope my question makes sense, I'm not really familiar with this time period and/or the legal background.
In theory, yes. In practice? Killing people without justification incurs wrath. A king that kills their subjects on a whim would be viewed tyrannically. A king that kills his kin would be viewed far worse than that. If you were a king and you killed someone back then you better make damn sure they aren't from an important family. Kings back then relied on the loyalty of their vassals and without their support have nothing. So, sure you could kill that person but you could also face a revolt/assassination attempt for doing so. If the person was just an insignificant peasant though? There is more wiggle room because that person has no standing. Their ties are limited and typically it takes a lot of dead peasants to trigger a revolt by them. So basically: You have absolute power but you having that power means having the support of the nobility/the church. Killing nobility, kin or clergy is a good way to lose that support.