Replacing Giant Defy 4 2013 alloy steerer fork with Giant carbon steerer fork I am planning on making the above replacement.

The original fork is the composite fork with alloy steerer, however the replacement (from Giant) has a carbon steerer. Can I still use the same original headset?
As other have stated you should be able to use the old headset providing it is in good condition. If you are swapping forks due to an accident then replace the headset even if it feels smooth. Your alloy steerer likely used a "star fangled nut " to apply the headset preload. With a carbon steerer you need a expandable plug that is made for use with carbon steerers.