I would assume he serves at the pleasure of the president like any appointee and that he would have been replaced by the Trump administration in any case.
Yep. Not really news. He’s just the first. A president appoints around 2,000 people. AFAIK, they all offer resignations to a new Administration, though some will be kept on anyway.
Some of the people in these kinds of positions are truly non-partisan and ask or are asked to be considered to continue in their jobs, but Clapper is not one of these.