None. The Shadow Proclamation, so far as we can tell, had no role in the Last Great Time War (assuming that's the time war you're referring to; the Last Great was by no means the only Time War).
We actually have no indication that the Shadow Proclamation is exceptionally powerful, much less the "highest authority in the universe." It's a strictly galactic organisation that hires mercenaries to do its police work. A war between what have been stated as the two most powerful societies in the universe is a bit out of their bailiwick.
At any rate, the LGTW took place entirely off-screen except for what little we see in "Day of the Doctor" and there's no indication the Proclamation existed prior to the War, so it's quite probable that the organisation formed in the power vacuum left by the Time Lords' absence.