The High Council was the Governing body at the top of the Federation's hierarchy. The President of the Federation was a "ruler of the High Council" amongst other things stated in the title (TV: Rumours of Death).
For the Forbidden Zone's defences to be disactivated, Servalan had to contact the High Council. (TV: Pressure Point)
Senator Bercol stated that he was head of the Information Bureau and "ex officio member of the High Council". (TV: Trial)
Durkim was summoned to a meeting of the High Council, a summons he called "a Presidential order-in-Council". Servalan refused to give him clearance to leave her command station. (TV: Star One)
Following the Intergalactic War, there was a High Council or at least some form of it with Servalan in power. Chesku was a High Councillor, although his wife Sula apparently was not. (TV: Rumours of Death)
However, Practor told Leitz of how the High Council was restored to power at the time Servalan was deposed (TV: Traitor).
Ardus wanted authorisation from the High Council to disclose information on Bucol-2. Sleer threatened his family, forcing him to change his mind. (TV: Animals)
Orac informed the crew that the authorities had placed a formal application for Federation membership before the High Council on Earth. Blake and his allies were expecting a High Council representative to arrive on the planet at any moment. (TV: Blake)