You may struggle to find land to rent for such use. My knowledge is of England, however, and things may differ in Scotland. Here, land is categorised by use and if landowners want their subsidies, they don’t have leeway to change the use. So, grazing land would only be available for grazing use, and agricultural grazing use at that. I’m not sure whether rabbits would qualify. Digging and pigs certainly wouldn’t. If you want land on which you can grow veg, then you’re not looking for pasture land but arable, and so on.
I don’t know how much land you’d be looking to get the use of, but you might do better to ask and look around for non-farming folks with a little bit of land - an acre or five - that’s getting away from them, and offer a mutually beneficial arrangement where you and your pigs clear the land, cultivate it, and so on.