I don't know about NZ clocks, but
www.timeanddate.com show them as going forward by one hour.
UK clocks go
Forward,
PV. The link to remember it is:
"We leap
forward into summer and fall
back away from winter"
(unfortunately, the italics here only slope forward not kcab)
So, it looks as if we both step forward by one hour. But it's possible that we do them on different days and that will cause the offset to increase for a while - as happened this year with Europe and the USA. Previously, they had synchronised with Europe and then decided not to any more. I sit to be corrected.