The NZ Arboricultural Association has released an update on the RMA amendments and what it will mean for the protection of urban trees (see details here). Apparently, in a surprise last minute change during the recent debating of the Bill, 'trimming' of trees protected under general urban tree protection rules will be permitted as of 1 October 2009. Unfortunately 'trimming' was not defined under the Act so its meaning will have to be determined by each individual council.
It might pay to check out the NZ Arb website and your local council before your start your own "trimming".