We are told in Brachot that R. Yishmael Ben Elisa was Maktir Ketoret Lifnai V'lifnim. This would mean that he must have served as a Kohen Gadol during the time that the Bet HAMikdash was still in use and standing. However, elsewhere in Shas we are told that R. Yishmael Ben Elisha was a small child (who was to grow into a talmid chacham) at the time of the Churban. How is this possible?
(a) Rebbi Yishmael Ben Elisha lived in the time of the Beis ha'Mikdash. When the Gemara in Gitin (58a) mentions that he lived at the time of the Churban, it must be referring to the grandson of Rebbi Yishma'el Ben Elisha of our Gemara (who had the same name) since otherwise there will be a blatant contradiction in the Gemara there in Gitin. A few lines later it tells the story of "the son and daughter of Rebbi Yishmael Ben Elisha Kohen Gadol" who were adults at the time of the Churban! It must be that that child was the grandson of the Rebbi Yishmael Ben Elisha who had served as Kohen Gadol, and his father was also Elisha (M. Kornfeld).
(b) Alternatively, the young Rebbi Yishmael was redeemed from prison by Rebbi Yehoshua 20 years or so before the Churban, when the Jews were already being oppressed. (E. Chrysler)