See tet’s post 66.
“Properly speaking karma effects your transition
from one life to the next but that is not understood
by most westerners.”
“Everybody was going on about karma … But it occurred to me that karma is instant as well as it influences your past life or your future life … I’m fascinated by commercials, as an art form … So the idea of instant karma was like the idea of instant coffee: presenting something in a new form.”
– John Lennon to Playboy magazine, 1980
If you accept reincarnation, then of course karma effects your next life, in the same way it effects this life - because it effects YOU, through what you've done.
But karma doesn't create reincarnation, and doesn't need reincarnation. And reincarnation doesn't need karma. But if karma exists, and reincarnation exists, then naturally karma will follow info the next life, because its attached to the person, the soul, not the body. And the soul doesn't die. And the soul is what earns karma through its actions.