The NZ Organisms Register lists five species of Anthopleura known from New Zealand (http://www.nzor.org.nz/search?query=anthopleura).
Parry: A KEY T O T H E COMMON NEW ZEALAND ANEMONES
Warts large at the top of the column, becoming smaller and almost disappearing at the base. Fusion of the top two or three warts, surmounted by marginal spherules. Fairly small—1-3 cm. Brown, with white and yellow markings. Lives in mud flats and rock pools. Anthopleura areoradiata.
White column, tentacles brown and white, but both may be pink or orange. Anthopleura inconspicua.
Column cream or orange, disc white to pink, tentacles pink. Anthopleura rosea.
Column dark red, tentacles and disc brown and white. Spherules pink, commonly in mussel beds. Anthopleura minima.
Complex fusion of warts at top of the column, involving ten or so warts, surmounted by a prominent marginal spherule, usually white. Column thick and muscular. Height about 10 cm. Oulactis muscosa.
Comparison of the Anthopleura species, based on Table 2 by Spano & Häussermann, Anthopleura radians, a new species of sea anemone (Cnidaria: Actiniaria: Actiniidae) from northern Chile, with comments on other species of the genus from the South Pacific Ocean" - Biodiversity and Natural History (2017) Vol. 3, No. 1, 1-11: