My understanding is that nothing moves faster than light, so an exploding star would not be noticed by us until its light reached us. Other emanations, radiations, shock waves, would reach us after that. It is possible, according to some theories, that there is information that travels instantaneously, though I don’t quite know what they mean by that. There is also the possibility of quantum entanglement, when whatever happens to one entangled entity happens to its entangled ‘twin’ instantaneously, even at distances of billions of light years.

The film, The Martian, used the finite speed of light/radiation in having radio communications between Mars and Earth and the spaceship having a delay between sending and receiving.