The Goldilocks zone will depend on the star's temperature and therefore how much its energy output is, so yes over time it will shift. To take an extreme example, our Sun's late life stage will see it expand and swallow up the earth; clearly we will no longer be in the zone when that happens.

So yes, the zone will shift but the lifespan of a star is so long that it won't change on a human (or even humanity's) timescale for most stars.