The reality is that in today's environment with change all around us, you don't have that time. The trick is to build those relationships at the same time you are pushing your agenda for your division, institution, etc. Show that you have a sense of humor and be able to laugh at yourself. It's okay to show people that you can make mistakes and can laugh at them. Send notes, birthday cards, e-mails.
People love to receive birthday cards.
They appreciate notes and e-mails when they have done something special or deserving of special recognition. If they have had a bad day or have some adversity in their lives, they especially need a word from you. This takes time and we all need to do a better job of this. Embrace and lead change. In case you haven't noticed, change is all around us.