At the council, the new Monarch (presumably Charles) will swear loyalty to Parliament, and to the Church of England. He will also become the new Supreme Governor of the church. (Catholics cannot ascend to the throne.)
The council will also make a "Proclamation of Accession," to be read out on "Proclamation Day" soon after the death in London Edinburgh, Windsor, York, and other towns and villages throughout the country.
This was the most recent Proclamation, from when Queen Elizabeth II ascended to the throne:
"Whereas it has pleased Almighty God to call to His Mercy our late Sovereign Lord King George the Sixth of Blessed and Glorious memory, by whose Decease the Crown is solely and rightfully come to the High and Mighty Princess Elizabeth Alexandra Mary:
"WE, therefore, the Lords Spiritual and Temporal of this Realm, being here assisted with these His late Majesty's Privy Council, with representatives of other Members of the Commonwealth, with other Principal Gentlemen of Quality, with the Lord Mayor, Aldermen, and Citizens of London, do now hereby with one voice and Consent of Tongue and Heart publish and proclaim that the High and Mighty Princess Elizabeth Alexandra Mary is now, by the death of our late Sovereign of happy memory, become Queen Elizabeth the Second, by the Grace of God Queen of this Realm and of all Her other Realms and Territories, Head of the Commonwealth, Defender of the Faith, to whom Her lieges do acknowledge all Faith and constant Obedience with hearty and humble Affection, beseeching God by whom Kings and Queens do reign, to bless the Royal Princess Elizabeth the Second with long and happy Years to reign over us."