As it is pot grown, you can easily leave the plant in its pot for a few days/weeks before planting it. Just ensure you keep the plant well-watered, and it gets enough sun. Don't leave it for too long, however, as you don't want the roots becoming root bound.
Though it is a great low maintenance hedge, the New Zealand Privet is dependant on the age of the hedge when it comes to pruning times.
Regarding newly planted Griselinia littoralis (planted in the winter), you can carry out some pruning in Spring and then again in the next two following Spring seasons. Once it has then become more mature, the hedge can be pruned in the summer, on an annual basis, just to ensure you are keeping it to its best desired shape.
The pruning is simple, and you are only required to remove any dead, diseased or damaged shoots (along with the general trim to maintain its shape). Your New Zealand Privet is also likely to benefit from a feed or mulch once you have done your pruning, as to help the hedge recover and flourish.