Public administrators have many responsibilities. However, if you want the key responsibilities, then there are three that stand out: competency, transparency, and honesty.
All workers, not just public ones, need to be competent. An administrator is paid to perform a task and he or she must do this task well. This person must remember that he or she is working for the people and has a job to perform.
Second, since governments are complex organizations, there needs to be transparency. To gain the trust of the people, the people must be in the know. In other words, the people need to keep this person accountable.
Finally, any public figure to retain the trust of the people has to be honest. This trait might be the most important.