Victoria Duff makes a very insightful remark in an article at Chron. She says that while being a staffer is about pleasing the supervisor, being a supervisor is about using your staffers to the best of their ability. Business success really is a two-way street.
With internal promotion, your first task is to manage your changed relationships with colleagues. However, with external promotion, you have to simultaneously build relationships with new colleagues while also proving that you deserve to be there in the first place. When you enter a new company, people generally expect some sizable changes, so use that knowledge wisely. It boils down to having confidence and being realistic. Take control of the situation while respecting your staff, and delegate work thoughtfully. You can read more here: http://work.chron.com/making-transition-staff-supervisor-4664.html