Hi,
Article 17 of the UK/New Zealand double taxation agreement advises that full relief is available for UK pensions/annuities, including trivial commutation lumps sum payments, including state pensions, but not incapacity benefit. To claim tax relief on your pensions, you will need to complete 'DT indiviual UK/New Zealand', which can be found here:
Double Taxation: UK-New Zealand (SI 1984 number 365 and protocols) (Form New Zealand-Individual)
Please complete all relevant sections of the form, declaring your pensions and send the signed and dated form to the New Zealand tax authorities. The New Zealand tax authorities will review the form and validate it with an official datestamp and the signature of an authorised individual. They will return the form to you, for onward transmission to HM Revenue and Customs.
Thank you.