For someone who is honest and follows good moral standards, use the adjective ethical. An ethical teacher will grade your papers honestly — even if she catches you sticking your tongue out at her.
Ethical comes from the Greek ethos "moral character" and describes a person or behavior as right in the moral sense - truthful, fair, and honest. Sometimes the word is used for people who follow the moral standards of their profession. An ethical lawyer or doctor does not try to take advantage of the client or patient's unfortunate situation. If something has happened and you are not sure what the right thing to do is, you are having an ethical dilemma.