"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.

thank you Stephan. Your answer really helped me.

The sentence would read like this: "the role of the British monarch is confined to that of head of the Commonwealth." "Head of head of the Commonwealth" makes no sense, but if you wanted to change the meaning of the sentence you could say, "the role of the British monarch is confined to head of THE head of the Commonwealth."

Thank you Marta. Do you mean it is possible to say like this: "head of head of the Commonwealth" if "that" refers to "head"?

"that of" is correct. "that" refers to the head of the Commonwealth. "with is" doesn't make any sense.