In addition to the well known statement by Jesus that John the Baptist was Elijah (not “in the succession of” or “like”, but WAS) there are other clear references such as in Romans where, speaking of the deceased hero’s of the OT it is said, “…they could have found a way to return…”. I did not go to the effort to find chapter and verse, but for anyone interested it won’t hurt to do your own research. There are other statements equally as revealing.
The fact of church acceptance of reincarnation for its first three hundred years is well established.