A dead Hand, and a king rides north
Jon Arryn dies in King's Landing and Robert rides to Winterfell to ask his oldest friend to replace him. Ned Stark takes a job he does not want, in a city that will kill him, because the alternative is refusing a king. In the same weeks a ranging beyond the Wall meets something that should not exist, and nobody who matters hears about it.
The fuller tale
Jon Arryn had been Hand of the King for seventeen years and had held the realm together for most of them, and he died suddenly of a fever nobody had heard of. His last words were about a book. His widow fled the capital with their son before the body was cold and wrote to her sister in Winterfell that the Lannisters had killed him.
So the king rode north ÔÇö a thousand riders, a wheelhouse, a queen who did not want to be there ÔÇö to ask his oldest friend to take the job. Ned Stark did not want it either. He took it because refusing a king is not a thing a Stark does, and because Robert asked him in the crypts with a hand on his sister's tomb, which was not an accident.
In the same weeks, a ranging beyond the Wall found something that should not exist, and one man survived it and ran, and was beheaded as a deserter by the very lord who was about to leave for the south. Nobody who mattered heard about it. That is the shape of the whole story in one season: the war everyone is watching, and the war nobody is.
The job that kills you
Being Hand of the King under Robert Baratheon meant doing all the ruling while the king hunted, and doing it in a city where every other person on the small council was running a private operation. Ned Stark arrived with a northern lord's assumptions about how truth works and began asking questions in a place where the answer to a question is a lever.
He was warned by nearly everyone, in nearly plain terms, and could not hear it. It is not stupidity ÔÇö he was not a stupid man ÔÇö it is a category error about what kind of place he was in.
Elsewhere in the wiki
 See the world as it stood in 298 AC What became of it  if an ending is written, it is here. Spoilers.
The chronicle records no ending here ÔÇö or none the maesters have set down.