Astar is 10 light years away from the earth. Suppose it brightens up suddenly today, after how long can we see this change?

The phrase "light year" is a distance ... it's the distance that light travels through vacuum in one year.

When you look at an object located 1 light year away from you, you see it as it was 1 year ago.

If a star located 10 light years away from us suddenly brightens, or dims, or explodes, we see the event 10 years later.