Sealion planning didn't extend to post-invasion planning, it was a placeholder project cooked up when Britain didn't fold as expected in July 1940. There was only a slim chance that it would have been authorised and its prospects of success were similarly remote.
There were broad outlines of what the Nazis would require from Britain in the event of armistice negotiations, however. The first would be a change of government, in which Churchill and his supporters would be replaced, most likely by former prime minister and wartime leader David Lloyd George, who had become an admirer of Hitler in the 30s and thought the war was as good as lost (as late as October 1940 he was anticipating the collapse of the Churchill government and his return to make peace). It is possible that George VI would have been replaced as King, with the Germanophile Duke of Windsor (Edward VIII, prior to the Abdication Crisis) making his return (recent research has uncovered further evidence of his close ties to the Nazis). While Hitler talked often about his desire to preserve Britain and the empire, in practice this new government would in the course of negotiations be arm-twisted into dismantling or surrendering Britain's sea and air defences, amongst other concessions.
Kershaw, Ian Fateful Choices: Ten Decisions that Changed the World, 1940-1941
It's unclear what the governmental structure of a conquered Britain would have been, but the RSHA (Reich Main Security Office, which was a subordinate agency of the SS and the parent agency of the Gestapo and SD) under Reinhard Heydrich did start planning for their own activities in Britain. Heydrich appointed RSHA administrator Dr. Franz Six as the agency's top official in Britain, where he would have oversight over six Einsatzgruppen based in London, Manchester, Birmingham, Bristol, Liverpool, and Edinburgh/Glasgow and charged with the suppression of resistance and the monitoring/elimination of the Jewish population.
The RSHA also assembled the Sonderfahndungsliste G.B. (Special Search List G.B, known after the war as The Black Book), which named almost 3,000 Britons and foreigners living in Britain who were to be immediately arrested following a successful invasion (the SD officer who assembled the document, Walter Schellenberg, was captured by the British at the end of the war and extensively interrogated). These included Winston Churchill, Clement Attlee, H. G. Wells, Stefan Zweig, Vera Brittain, Noel Coward, Anthony Eden, E. M. Forster, Megan lloyd George (though not her father David Lloyd George, who is speculated to have been a possible choice as leader of the puppet government, akin to Philippe Petain in Vichy France), Bertrand Russell, Leonard and Virginia Woolf, and all the heads of the governments-in-exile in Britain. Interestingly, it also included Sigmund Freud and Alduous Huxley. Freud had been dead for a year when the document was written and Huxley had emigrated to the United States in 1936, so the Special Search List G.B. wasn't the most thoroughly-researched document to come out of the Nazi government.
Sources:
Robert Gerwarth, Hitler's Hangman: The Life of Heydrich.
Walter Schellenberg, The Schellenberg Memoirs.
Also, I believe it's discussed in Shirer's The Rise and Fall of the Third Reich.