His Contract has already been extended once (he has been in post for 8 years when, I think the norm is 5-6 years). She wanted someone she could work with for the whole of her term. He has said he did not agree with the election of Police and Crime Commissioners so in my opinion he waited until the day after she had been sworn in and then announced he was leaving.
There has been a similar problem with the new Mayor in Bristol. An independent candidate was elected and offered the Labour party 3 seats in his cabinet, with 1 each going to the Liberals, Conservatives and Greens. The local Labour party voted against taking up those seats, proving they were more interested in their party than they were in what was good for the city of Bristol. It was only after they realised that the people of the city were pretty disgusted by their attitude that they did an about turn and have now said they will take seats. I don't mind betting that they will do everything they can to stop the new Mayor from putting in place his ideas.