You might find that as the privet is a greedy feeder, it has taken a lot of the goodness out of the soil, so in the land near to the hedge you might need to manure/fertilise/mulch more heavily - the same goes for watering.
But on ;the plus side, it will attract lots of small hedgerow birds who will help keep bugs at bay, and when it blooms it will attract lots of pollinating insect - I love privet - the smell of privet always takes me back to an idyllic holiday in Brittany years ago.