Manage in both directions. You're new on the job and feeling pretty tense about proving yourself, so your first impulse will be to invest your time in managing up, trying to do what the brass expects of you. Not a bad idea, but don't be lopsided about it. Your best results will come from dividing your time evenly between the bosses and the bossed. Many a new exec has won the battle of impressing his or her superiors, but lost the war of fielding a consistently winning team by instinctively looking up rather than both up and down.
Leadership is never easy.
But these four steps will go a long way toward having your new team fighting for you and your goals, rather than against you.