"nip 'round" or "take a nip 'round", simply means to go to some place, not necessarily at any particular speed, but usually soon. It can be in a vehicle or on foot. It is British slang, seen sometimes in American English, but not very often, even though most Americans would understand it. "I didn't see the package. They should have put it by the front door." "Nip round back and see if it's there" (or "Take a nip round back...")

It just means to come over, another way of saying it is, pop over and see me.

it means to go somewhere quickly or be somewhere for only a short time. cowboy...