You can use the word senior to describe anyone who's older than you are. You might say, "My brother is six years my senior," especially if you want to make him feel old.
Senior means "older," but it also means "old or aged," like your grandmother, who despite being a senior citizen, continues her skydiving hobby. A senior is also a student in the final year of either high school or college, or an authority: "She holds a senior position in the State Department." The Latin word senior means "older," and it's the basis of respectful terms in many languages, like señor in Spanish and sire in French.