"That of". "That" refers to the role.( It's not actually true though. The more important role is as head of state of several countries, including the UK.)
You can't use "who" to refer to a preposition, only to a person. There could conceivably be a preposition intervening in some cases (perhaps particularly with phrasal verbs?), e.g. "They beat the guy up, who was hiding in the corner". That's not the case in your sentence, though; "who is" is wrong here.