Like any non-lawyer, you may provide 'legal services', but not in the 'reserved areas of work' as defined in s6 of the Lawyers and Conveyancers Act (LCA). You can also do certain things which are, by statute, able to be done by 'an enrolled barrister and solicitor'. These include taking statutory declarations – see s9 of the Oaths and Declarations Act.
You should take care to describe yourself in a way that will not be in breach of s21 of the LCA. One suitable formula might be 'Enrolled barrister and solicitor of the High Court of New Zealand'.
If you provide any legal services without a current practising certificate you must not describe yourself as a lawyer - or law practitioner, legal practitioner, barrister, barrister and solicitor, solicitor, attorney-at-law or counsel. To do so is an offence under s21 of the LCA.
Note, though, that the situation is different for lawyers admitted in other jurisdictions.