I was watching a relativity video, and although I am not sure, I felt that it was trying to tell that the effect of gravitation of a body is instantaneous, in the sense that a sudden change in the mass of a body will instantaneously be felt by any object at a distance, even before light can be exchanged between them. So I want to make sure if its true. You don’t have to explain me why this is so if you don’t wish to. Also, please tell me if this has been experimentally established, or it is just a theory.
W.r.t your original question, yes, we would feel the gravitational effects for 10 years from now. Changes in space-time propagate at the speed of light, so spacetime here would still be warped due to that star's gravity even if it disappeared today.