For the two commonest varieties of privet, hardwood cuttings in early winter, so end of October really, but if the weather cools in the next couple of weeks, you can do it then.

Thanks Bamboo, should I just replant the cutting in a pot with soil I do I need to put it in water first? Thanks again.

Look up the method on Google if you don't have a book - google hardwood cuttings - should be info, maybe even a video, as to how to do it. Best placed in a trench outside in the ground in an out of the way bit of the garden, they'll be there a year.