I will repeat, the Chief Rabbi is not for the Charedim, they have their own Rabbanim, ie the Belz answer to the Belzer Rebbe, the Ger to the Gerrer Rebbe, the LItvish to Rav Shteinmen The Sefardic Charedim to Rav Yosef etc this wouldnt change no matter who is the chief Rabbi
The Chief rabbi is for chilonim and deals with their religious issues and issues related to the government