“Put them in mind to be  subject to principalities and powers,”
With all authority, we are to put believers “in mind”. This phrase implies that we are to suggest an action of the memory in the lives of others. We are to remind quietly certain actions of life. As we would do it, others might follow our pattern.
“To be subject” implies that we are not to live unto ourselves. Our principle of life is not to be libertarian but to be subject or subordinate to the righteousness ways of God. Our pattern of living is to obey proper authority.
To whom has God placed man under to be subordinate?
It is principalities and powers. These are authorities placed over us by God.
Principality implies that our lives are to be ordered lives. They commence from a beginning and continue according to an ordered plan in time. There is implied precedence laid out for us. There is implied oversight by a chief to whom we are subject.
A power is one who is able, he is privileged by God to delegate influence. He is given right to exercise this publicly. Its purpose is to restrain evil and to promote good. Even this power is limited with implied obligation to do all within the will of God.