"an elderly man," is a longer form of presbus, the comparative degree of which is presbuteros, "a senior, elder," both of which, as also the verb presbeuo, "to be elder, to be an ambassador," are derived from proeisbaino, "to be far advanced." The noun is found in Luk 1:18, "an old man;" Tit 2:2, "aged men," and Phm 1:9, where the RV marg., "Paul an ambassador," is to be accepted, the original almost certainly being presbeutes (not presbutes), "an ambassador." So he describes himself in Eph 6:20. As Lightfoot points out, he is hardly likely to have made his age a ground of appeal to Philemon, who, if he was the father of Archippus, cannot have been much younger than Paul himself. See OLD.
the feminine of No. 1, "an aged woman," is found in Tit 2:3. from geras, "old age," signifies "to grow old," Joh 21:18 ("when thou shalt be old") and Heb 8:13 (RV, "that which... waxeth aged," AV, "old"). See OLD.