Hi Jacqui,
The compost you add on top of your beds rots down/gets brought down by worms over the course of the year such that by the time you come to add a layer for your next crop little if any is left of your original layer. Even an initial layer of 6″ over grass pasture, which you would do with new ground you wish to cultivate, will have been reduced to little more than an inch after 9-12 months.
In your own case you will only need to add 1-2″ of compost on top of your current beds and this will rot down and be incorporated into the soil very quickly, 6-9 months.
I don’t know if you previously dug in compost to your beds but no dig is simply (very simplistically) a different way of applying compost and getting the worms to do the digging for you.
Don.
