What's the context? If you're in the fashion trade and talking to a factory, there are probably standard terms in use. If so, I am afraid I don't know them, but maybe someone else will.
I'd use 'raise/lower the waistband' ("Could you lower the waistband on this dress so it's just over my hips?") if it means simply moving the waistband up/down - there you go, I've just inadvertently used both. I think though that 'move up/down' is more colloquial.