How can you stop the itch after shaving your privets?

Trim Hedge or Bush??: I'm not entirely sure what you meant. I'll try to answer anyway. A privet is a hedge plant in the ligustrum family there have been reported cases of contact dermatitis from the sap of these plant contracted while trimming. If so then a Hydrocortisone cream may be helpful. If shaving is real operative word then "private" parts would benefit from a moisturizing cream or a applying hair conditioner.