Eliyahu is told by Hashem to anoint Elisha to be his successor as a prophet (Kings 1:19:16).
Yesha'ayahu (8:2) prophesied of two future prophets: Zechariah ben Yevarchiyahu and Uriah Hakohen. Zechariah lived centuries later, in the beginning of the Second Temple era, but Uriah might have already been alive at the time - his prophecy was brought in the Book of Micha 3:12, according to the Talmud in Makot 24b and Micha lived around the time of Yesha'ayahu and may have even been his student (he paraphrases him a number of times).
Yirmiyahu (26:17-24) mentions two past prophets: Micha (of the Book of Micha) and Uriyahu ben Shma'ayahu.
Malachi (3:23) foretells the return of Eliyahu. During this time, Eliyahu will reconcile parents with children and children with parents.