The picture of this verse is that of the athletic contests of the day. It pictures strenuous training and vigorous exercising. For the persons who have allowed God's discipline to train them, there is the result of righteousness and peace. Righteousness is that which sets us in right relationship with God. God's discipline, rightly borne, will bring us to the place where we are right with God.
Peace is used here as an adjective, a descriptive word.
It is saying that the Christian who is trained by God's discipline will be a peaceful person, a person characterized by peace. Suffering does not bring us peace but makes us irritable and short-tempered. It makes us susceptible to anger and frustration. This brings us peace, even in the midst of the struggles and sufferings of life. This is what characterized Jesus at the time of His greatest struggle and suffering.