Though not an expert on the bible, my personal interpretation suggests that the concept of reincarnation (life after life) is alluded to in both the New and Old Testaments.   Although reincarnation is not explicitly taught by Jesus, like a number of other theological/cosmological concepts, neither does it explicitly deny the concept of reincarnation - in my opinion. 

From an Open Source Religion point of view, the concept of reincarnation would be considered as foundational from a wide number of theological perspectives.  After all, it is a concept already central in Eastern Religious traditions - such as "Hinduism" and Buddhism and, as the video below suggests, this concept should also be included in the "ancient" mystical Jewish (oral) tradition - where the concept of reincarnation was extended, I speculate, from "Hinduism" into its offshoot - Buddhism and also from Ancient Israel into early Christianity from it's parent religion - Judaism. But why is this ancient tradition or understanding not remembered by Christians and how did this happen? 

It seems that when Western Christianity (Church of Rome) was adopted by the fading vestiges of the Roman Empire, as it's "official religion", the mystical traditions within the Christian Churches of both Egyptian and  Eastern Church traditions were alienated" as heretical and subsequently forgotten.

But why was the metaphysical doctrine of reincarnation important and why was it subsequently dropped from the modern Christian era?

In a comprehensive world view, one would consider that the universe is created by happenstance (a benign fluke) or our of something or for a reason.  Is the universe an arbitrary happenstance?  If your conclusion is "No", it is not an arbitrary happenstance, a subsequent question then becomes apparent - "Why was the blind man born blind?" Is there a reason why?

To Jews, "Hindus" Buddhists and more, one's station in life is considered to be a consequence of one's own actions?  The Roman Church saysd otherwise.  But, it provides very little explanation of, for example, why a man would be born this way. Christianity does, alternatively, provide (the free gift of) salvation to the blind man who was somehow not given a life without the gift of sight.  Was this deemed so in order that the non-sighted one could be some kind of lesson to us all?  If so, what is the lesson and what criteria precipitated this lesson - and for whose benefit was it - - and WHY?.

Was the blind man given the gift of free will, as well as, a handicap with which to apply it?  Was this soul then somehow created in God's image?  And by what criteria are we expected to understand or believe in how this cosmology works? 

In the following, Jewish Rabbi Trugman speaks on Reincarnation in the Jewish Tradition.