Karma means many things to many people.
First let's bring a few things together – science and religion. Strange bedfellows truth seekers are.
NDE research suggests that we remember everything after death but not the way we experience memories here normally. Here we remember events; this happened and that happened, I had that for breakfast, this happened on the way to work. The memory we have in the afterlife is different. It's more like what we have when we are in a time of great joy or turmoil or anniversaries or holy days - times when we remember how we got here, our great appreciation of who affected our lives whether close at hand or from across history. It is a memory governed by what matters to us. But NDE research suggests it goes further. We not only remember things we went through, we also experience how it affected others - how we affected them with our choices both mindless and mindful but again not in the way of a series of events but in a manner of the importance and meaning of those interactions. NDE also suggests that the value of all these is measured in spiritual terms - the ability to bring forth virtues of love, courage, caring, kindness, and sacrifice. It is measured by giving and accepting, understanding or awareness - actions taken and not taken. Renee Pasarow, one who has shared her extreme experience, speaks of this dynamic of memory, at Lightafterlife.com (about 3/4ths in part 1 where she describes both general and a specific case in a daycare camp.) Baha'i scripture also speaks to these things in similar form. Here's just one quote: "And now concerning thy question regarding the soul of man and its survival after death.… the soul… will continue to progress … It will endure as long as the Kingdom of God… will endure.… that soul will freely converse, and will recount … that which it hath been made to endure in the path of God.…" So it is agreed we remember everything, and the meaning of everything to ourselves and to each other as we affected each other. This speaks an aspect of karma - that our deeds are measured and credit and debt are counted. "Bring thyself to account each day ere thou art summoned to a reckoning; for death, unheralded, shall come upon thee and thou shalt be called to give account for thy deeds." He says again.
So both in this life and beyond we are to take into account how we have made choices or not and affected others and ourselves. So in the sense that our deeds are noted and recalled and we get the deserts of our choices both evidence and scripture support it. So in the sense that karma deals with things actually mattering, that it comes back to us, yes there is something one can call Karma.
Some versions of the topic of Karma also deal with reincarnation - the idea being that the summary of good and bad we were responsible for previously affects our present lives. Generally speaking far eastern religions (Hinduism and Buddhism) support reincarnation and near eastern religions (Abrahamic) do not. This is complicated by the fact that the religions evolved over time. Even in Hinduism there is no mention of reincarnation at first and instead there are indicators of death being final. Another part of the problem is that in the west we are only getting some of the discussion of what the other far eastern religions are like. Buddhism, for example, is as divided into groups as Christianity. So where Christianity has Catholic, Protestant, and groups neither accepts so too are Buddhists segregated into groups - ranging from pure atheists to a mixed case, to pure theists who claim a Buddha as a personal savior. So across the evolution of religions and what we are likely to hear about in the west we are sometimes pretty far from how things began.
The subject is also part of psychic and NDE research with some taking it completely as real and some taking it completely as false. Few have taken care to review the evidence carefully. One NDE researcher, Phyllis Atwater, in “Coming Back to Life” (p. 143-4) after performing and experiencing past life regression came to feel that the attitude of the hypnotist seemed to be the leading indicator on what people experienced and no technique seemed to get round that, though profound healing could be achieved, whatever the facts were. David Fontana in “Is there an Afterlife” (p. 440-2) reviewed the available research and though something of past life regressions seems to be legitimate in terms of information content it was impossible to determine if these were the experiences of the same identity, or simply those of other identities with whom they were connected “beads on the same necklace and the memory they share is contained in the string.”
Never the less there are ideas of return that do appear in various ways in scripture. There is a way to bridge the gap and take into account both points of view. I first thought of this when I was wrestling with a topic in Baha’i scripture, (see a discussion of multiple kinds of “return”.) So on the one hand you have the return specified and at the same time there are denials of personally, individually, returning. So for example on the one hand Jesus says that John the Baptist was the return of Elijah and on the other John the Baptist says he was not Elijah. People argue about this in every direction. John just didn't know what he was talking about and he was the reincarnation, or this is just one example of the contradictions of the Bible, or it was just symbolic and prophetic but had no real meaning in itself. I think all these are wrong.
Think of it like this. We all play roles in life. We are fathers or mothers, friends, sons or daughters. We are bosses or employees. We serve as guides and helpers and we are guided and helped. There are only so many jobs, roles, we can play in the world and we shift among them all the time. Now above I emphasized that some things matter more than others and the spiritual emphasis is in how things matter. So to the extent we act in our roles with spiritual distinction and bring virtues to bear, we are acting in our roles well. And good or bad there are also others acting in their roles - across history, and every culture. Some of those roles are seemingly singular - like Jesus came - but become repeated - like Jesus will come again. And some are pretty crowded. But whatever role we play there are those like us - and we "get" them in ways we don't even have to talk about. We see what they go through and it's just like us. We read of some ancient event and we can see ourselves doing the same thing. There is a resonance. A kinship. I have done that. I know what that feels like from the inside. Even if we do not specifically see ourselves in roles others have inhabited sometimes these are pointed out to us. Thus Jesus saw John the Baptist in the role of Elijah even though of his own self he was not Elijah. Make sense? This is a natural capacity in fact - the basis of empathy.
Now there are also suggestions of one’s condition in this life being affected by the past; nature and nurture. We are given gifts and have to make our own choices. Consider - in the Bible there is the initial statement that the sins of the father are visited upon the sons which later evolves into a conditional statement that if one follows in the sins of the father the son too will suffer. A modern form of it might be called the cycle of poverty: on the negative side – and of primogenitary on the positive side - (hey, Jesus was in the station of the Son, remember?)