I’ve got a big piece of land, it is all fenced with a decently high fencing

As far as nature is concerned, no you don’t. There is just land. Animals don’t know nor care about property laws.

An electric fence won’t stop animals from digging underneath. It works with domesticated animals, but not so well with wild animals.

I reckon your best bet is to focus on the area of land where you wish to keep animals in rather than trying to keep animals out of the entirety of the land.

Repairing fencing is also just a chore of farming that you need to get used to. To reduce the chore, and aid nature at the same time, consider making hedges instead of fences. There’s many tutorial videos on various styles of English hedging if you want to give it a try.

And finally, despite capitalist agrochemical farming’s insistence, farming is about working with nature, not against it. Good luck!