How should I act upon discovering that my older brother smokes, knowing that there are no obvious signs of smoking on him?

You should advise your brother gently and wisely, explaining the prohibition of smoking and its harms, and showing him the words of the scholars on this matter. Conceal his affair and do not inform anyone of his disobedience. If he does not stop smoking after being advised, then it is permissible to inform someone who is hoped to help prevent him from this evil.