Create temporary gardensUsing raised beds in your garden will save you loads on garden preparation as you can add in good quality soil and start right away. You can try moveable systems such as pots, Vegepods or even home made containers using shipping crates. We have mostly used what was freely available to us and that's some corrugated iron raised beds. When we have to move we just pull down the bed and scatter the soil around the garden. You can read about our moving story here to one of my favourite garden setups here. You'll also be super surprised about what you can grow in a pot. We have all our fruit trees in pots and all of our herbs.
Be mindful if you do destroy a good quality lawn you may have to replace the turf when you leave. We have found that in most cases rental lawns are full of weeds and not very well looked after, but we always try to place our raised beds in spaces where the gardens we're anyway.